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Properties

Label 25200.q
Number of curves $6$
Conductor $25200$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("q1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 25200.q have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 25200.q do not have complex multiplication.

Modular form 25200.2.a.q

Copy content sage:E.q_eigenform(10)
 
\(q - q^{7} - 4 q^{11} + 2 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 25200.q

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.q1 25200be6 \([0, 0, 0, -2358075, -1393717750]\) \(62161150998242/1607445\) \(37498476960000000\) \([2]\) \(393216\) \(2.2869\)  
25200.q2 25200be4 \([0, 0, 0, -153075, -20002750]\) \(34008619684/4862025\) \(56710659600000000\) \([2, 2]\) \(196608\) \(1.9404\)  
25200.q3 25200be2 \([0, 0, 0, -40575, 2834750]\) \(2533446736/275625\) \(803722500000000\) \([2, 2]\) \(98304\) \(1.5938\)  
25200.q4 25200be1 \([0, 0, 0, -39450, 3015875]\) \(37256083456/525\) \(95681250000\) \([2]\) \(49152\) \(1.2472\) \(\Gamma_0(N)\)-optimal
25200.q5 25200be3 \([0, 0, 0, 53925, 14080250]\) \(1486779836/8203125\) \(-95681250000000000\) \([2]\) \(196608\) \(1.9404\)  
25200.q6 25200be5 \([0, 0, 0, 251925, -107887750]\) \(75798394558/259416045\) \(-6051657497760000000\) \([2]\) \(393216\) \(2.2869\)