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SageMath
E = EllipticCurve("mb1")
E.isogeny_class()
Elliptic curves in class 388080mb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.mb1 | 388080mb1 | \([0, 0, 0, -1684032, 841150219]\) | \(10392086293512192/1684375\) | \(85607294850000\) | \([2]\) | \(4792320\) | \(2.0753\) | \(\Gamma_0(N)\)-optimal |
| 388080.mb2 | 388080mb2 | \([0, 0, 0, -1678887, 846545266]\) | \(-643570518871152/8271484375\) | \(-6726287452500000000\) | \([2]\) | \(9584640\) | \(2.4219\) |
Rank
sage: E.rank()
The elliptic curves in class 388080mb have rank \(1\).
Complex multiplication
The elliptic curves in class 388080mb do not have complex multiplication.Modular form 388080.2.a.mb
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 Cremona 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 Cremona labels.
