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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 310464u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.u2 | 310464u1 | \([0, 0, 0, 59388, -63660800]\) | \(65939264/5021863\) | \(-1764170586945220608\) | \([2]\) | \(7077888\) | \(2.1807\) | \(\Gamma_0(N)\)-optimal |
310464.u1 | 310464u2 | \([0, 0, 0, -2075052, -1109536400]\) | \(351596839112/14235529\) | \(40007306533699878912\) | \([2]\) | \(14155776\) | \(2.5273\) |
Rank
sage: E.rank()
The elliptic curves in class 310464u have rank \(1\).
Complex multiplication
The elliptic curves in class 310464u do not have complex multiplication.Modular form 310464.2.a.u
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.