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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 363726.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363726.m1 | 363726m2 | \([1, -1, 0, -5910207, -5524547077]\) | \(654763446232875/591701374\) | \(20632411036825813962\) | \([2]\) | \(14376960\) | \(2.6303\) | |
| 363726.m2 | 363726m1 | \([1, -1, 0, -454317, -43559983]\) | \(297408796875/148481036\) | \(5177479553944268868\) | \([2]\) | \(7188480\) | \(2.2838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363726.m have rank \(1\).
Complex multiplication
The elliptic curves in class 363726.m do not have complex multiplication.Modular form 363726.2.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.
