Properties

Label 7800.t
Number of curves $4$
Conductor $7800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7800.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.t1 7800d4 \([0, 1, 0, -192408, 32342688]\) \(49235161015876/137109375\) \(2193750000000000\) \([2]\) \(36864\) \(1.8162\)  
7800.t2 7800d3 \([0, 1, 0, -179408, -29199312]\) \(39914580075556/172718325\) \(2763493200000000\) \([2]\) \(36864\) \(1.8162\)  
7800.t3 7800d2 \([0, 1, 0, -16908, 50688]\) \(133649126224/77000625\) \(308002500000000\) \([2, 2]\) \(18432\) \(1.4697\)  
7800.t4 7800d1 \([0, 1, 0, 4217, 8438]\) \(33165879296/19278675\) \(-4819668750000\) \([2]\) \(9216\) \(1.1231\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7800.t have rank \(0\).

Complex multiplication

The elliptic curves in class 7800.t do not have complex multiplication.

Modular form 7800.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.