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SageMath
E = EllipticCurve("pg1")
E.isogeny_class()
Elliptic curves in class 310464.pg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.pg1 | 310464pg2 | \([0, 0, 0, -32844, -897680]\) | \(59776471/29282\) | \(1919385928728576\) | \([2]\) | \(1179648\) | \(1.6259\) | |
310464.pg2 | 310464pg1 | \([0, 0, 0, 7476, -107408]\) | \(704969/484\) | \(-31725387251712\) | \([2]\) | \(589824\) | \(1.2793\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.pg have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.pg do not have complex multiplication.Modular form 310464.2.a.pg
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.