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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 310464.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.z1 | 310464z2 | \([0, 0, 0, -169932, -21046480]\) | \(193100552/43659\) | \(122698566098583552\) | \([2]\) | \(3932160\) | \(1.9918\) | |
310464.z2 | 310464z1 | \([0, 0, 0, 24108, -2030560]\) | \(4410944/7623\) | \(-2677944895008768\) | \([2]\) | \(1966080\) | \(1.6452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.z have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.z do not have complex multiplication.Modular form 310464.2.a.z
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.