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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 236691.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236691.o1 | 236691o1 | \([1, -1, 0, -1183509, -495012056]\) | \(10418796526321/6390657\) | \(112451839809475257\) | \([2]\) | \(5160960\) | \(2.2146\) | \(\Gamma_0(N)\)-optimal |
| 236691.o2 | 236691o2 | \([1, -1, 0, -962424, -685808411]\) | \(-5602762882081/8312741073\) | \(-146273384335701550473\) | \([2]\) | \(10321920\) | \(2.5611\) |
Rank
sage: E.rank()
The elliptic curves in class 236691.o have rank \(1\).
Complex multiplication
The elliptic curves in class 236691.o do not have complex multiplication.Modular form 236691.2.a.o
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.
