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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 72128.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.m1 | 72128u2 | \([0, 1, 0, -3325793, -341474561]\) | \(263822189935250/149429406721\) | \(2304274631402314661888\) | \([2]\) | \(2949120\) | \(2.7890\) | |
| 72128.m2 | 72128u1 | \([0, 1, 0, 821567, -42035169]\) | \(7953970437500/4703287687\) | \(-36263499732606189568\) | \([2]\) | \(1474560\) | \(2.4425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.m have rank \(1\).
Complex multiplication
The elliptic curves in class 72128.m do not have complex multiplication.Modular form 72128.2.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.
