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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 53130.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53130.m1 | 53130m4 | \([1, 1, 0, -10432802, -12974634234]\) | \(125581791038790971715422761/28639992150\) | \(28639992150\) | \([2]\) | \(1146880\) | \(2.2970\) | |
| 53130.m2 | 53130m3 | \([1, 1, 0, -671302, -190337534]\) | \(33456349027422149126761/3756619149206927850\) | \(3756619149206927850\) | \([2]\) | \(1146880\) | \(2.2970\) | |
| 53130.m3 | 53130m2 | \([1, 1, 0, -652052, -202930884]\) | \(30659950320867474674761/463009261522500\) | \(463009261522500\) | \([2, 2]\) | \(573440\) | \(1.9504\) | |
| 53130.m4 | 53130m1 | \([1, 1, 0, -39552, -3378384]\) | \(-6842994895178474761/922569243750000\) | \(-922569243750000\) | \([2]\) | \(286720\) | \(1.6038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53130.m have rank \(0\).
Complex multiplication
The elliptic curves in class 53130.m do not have complex multiplication.Modular form 53130.2.a.m
sage: E.q_eigenform(10)
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.
