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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 94136a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94136.b2 | 94136a1 | \([0, 1, 0, -560, -280976]\) | \(-4/7\) | \(-34048747199488\) | \([2]\) | \(281600\) | \(1.2755\) | \(\Gamma_0(N)\)-optimal |
| 94136.b1 | 94136a2 | \([0, 1, 0, -67800, -6736016]\) | \(3543122/49\) | \(476682460792832\) | \([2]\) | \(563200\) | \(1.6221\) |
Rank
sage: E.rank()
The elliptic curves in class 94136a have rank \(1\).
Complex multiplication
The elliptic curves in class 94136a do not have complex multiplication.Modular form 94136.2.a.a
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.
