↑

Properties

Label 3150.s
Number of curves $2$
Conductor $3150$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("s1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 3150.s have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 + 6 T + 13 T^{2}\) 1.13.g
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 3150.s do not have complex multiplication.

Modular form 3150.2.a.s

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} + 4 q^{11} - 6 q^{13} - q^{14} + q^{16} + 4 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 3150.s

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.s1 3150d1 \([1, -1, 0, -1152942, -475178284]\) \(551105805571803/1376829440\) \(423439591680000000\) \([2]\) \(80640\) \(2.2596\) \(\Gamma_0(N)\)-optimal
3150.s2 3150d2 \([1, -1, 0, -720942, -835898284]\) \(-134745327251163/903920796800\) \(-277998016303350000000\) \([2]\) \(161280\) \(2.6062\)