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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 30723.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30723.m1 | 30723k2 | \([0, -1, 1, -1473103, 688664514]\) | \(-3004935183806464000/2037123\) | \(-239665483827\) | \([]\) | \(194400\) | \(1.9331\) | |
| 30723.m2 | 30723k1 | \([0, -1, 1, -17803, 991605]\) | \(-5304438784000/497763387\) | \(-58561364717163\) | \([]\) | \(64800\) | \(1.3838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30723.m have rank \(1\).
Complex multiplication
The elliptic curves in class 30723.m do not have complex multiplication.Modular form 30723.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
