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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 56350.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56350.p1 | 56350d2 | \([1, -1, 0, -117081442, -487589266284]\) | \(281504613025066887/1354240\) | \(853882324120000000\) | \([2]\) | \(5419008\) | \(3.0633\) | |
56350.p2 | 56350d1 | \([1, -1, 0, -7321442, -7608786284]\) | \(68835304542087/150732800\) | \(95040815206400000000\) | \([2]\) | \(2709504\) | \(2.7167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56350.p have rank \(0\).
Complex multiplication
The elliptic curves in class 56350.p do not have complex multiplication.Modular form 56350.2.a.p
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.