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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 142956.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142956.m1 | 142956j2 | \([0, 0, 0, -170031, -25446890]\) | \(61918288/3971\) | \(34864945158599424\) | \([2]\) | \(1140480\) | \(1.9247\) | |
| 142956.m2 | 142956j1 | \([0, 0, 0, 8664, -1680455]\) | \(131072/2299\) | \(-1261560515607216\) | \([2]\) | \(570240\) | \(1.5781\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142956.m have rank \(0\).
Complex multiplication
The elliptic curves in class 142956.m do not have complex multiplication.Modular form 142956.2.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.
