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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 317680bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317680.bj1 | 317680bj1 | \([0, 0, 0, -13718, -596733]\) | \(379275264/15125\) | \(11385103202000\) | \([2]\) | \(580608\) | \(1.2718\) | \(\Gamma_0(N)\)-optimal |
317680.bj2 | 317680bj2 | \([0, 0, 0, 6137, -2181162]\) | \(2122416/171875\) | \(-2070018764000000\) | \([2]\) | \(1161216\) | \(1.6184\) |
Rank
sage: E.rank()
The elliptic curves in class 317680bj have rank \(1\).
Complex multiplication
The elliptic curves in class 317680bj do not have complex multiplication.Modular form 317680.2.a.bj
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.