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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 319580.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
319580.b1 | 319580b1 | \([0, 1, 0, -774841, 244581084]\) | \(5405726654464/407253125\) | \(3875898500802050000\) | \([2]\) | \(6021120\) | \(2.3120\) | \(\Gamma_0(N)\)-optimal |
319580.b2 | 319580b2 | \([0, 1, 0, 743164, 1087377460]\) | \(298091207216/3525390625\) | \(-536828047202500000000\) | \([2]\) | \(12042240\) | \(2.6586\) |
Rank
sage: E.rank()
The elliptic curves in class 319580.b have rank \(1\).
Complex multiplication
The elliptic curves in class 319580.b do not have complex multiplication.Modular form 319580.2.a.b
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.