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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 40656.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.m1 | 40656be2 | \([0, -1, 0, -3550664, 2571426288]\) | \(512576216027/1143072\) | \(11039965114559496192\) | \([2]\) | \(1520640\) | \(2.5365\) | |
| 40656.m2 | 40656be1 | \([0, -1, 0, -143304, 69061104]\) | \(-33698267/193536\) | \(-1869200442676740096\) | \([2]\) | \(760320\) | \(2.1899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40656.m have rank \(0\).
Complex multiplication
The elliptic curves in class 40656.m do not have complex multiplication.Modular form 40656.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
