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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 17424ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.f2 | 17424ce1 | \([0, 0, 0, -4719, -142054]\) | \(-4253392/729\) | \(-1991891886336\) | \([]\) | \(32256\) | \(1.0864\) | \(\Gamma_0(N)\)-optimal |
17424.f1 | 17424ce2 | \([0, 0, 0, -396759, -96191854]\) | \(-2527934627152/9\) | \(-24591257856\) | \([]\) | \(96768\) | \(1.6357\) |
Rank
sage: E.rank()
The elliptic curves in class 17424ce have rank \(0\).
Complex multiplication
The elliptic curves in class 17424ce do not have complex multiplication.Modular form 17424.2.a.ce
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.