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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 310464m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.m2 | 310464m1 | \([0, 0, 0, 24108, 2030560]\) | \(4410944/7623\) | \(-2677944895008768\) | \([2]\) | \(1966080\) | \(1.6452\) | \(\Gamma_0(N)\)-optimal |
310464.m1 | 310464m2 | \([0, 0, 0, -169932, 21046480]\) | \(193100552/43659\) | \(122698566098583552\) | \([2]\) | \(3932160\) | \(1.9918\) |
Rank
sage: E.rank()
The elliptic curves in class 310464m have rank \(1\).
Complex multiplication
The elliptic curves in class 310464m do not have complex multiplication.Modular form 310464.2.a.m
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.