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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 152460z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.d1 | 152460z1 | \([0, 0, 0, -615648, 185923397]\) | \(1248870793216/42525\) | \(878714806107600\) | \([2]\) | \(1344000\) | \(1.9591\) | \(\Gamma_0(N)\)-optimal |
152460.d2 | 152460z2 | \([0, 0, 0, -588423, 203113262]\) | \(-68150496976/14467005\) | \(-4783020432604888320\) | \([2]\) | \(2688000\) | \(2.3057\) |
Rank
sage: E.rank()
The elliptic curves in class 152460z have rank \(0\).
Complex multiplication
The elliptic curves in class 152460z do not have complex multiplication.Modular form 152460.2.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 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.