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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 414736.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.f1 | 414736f2 | \([0, 1, 0, -72172704, -235731277580]\) | \(582810602977/829472\) | \(59172093461645764984832\) | \([2]\) | \(48660480\) | \(3.2725\) | |
414736.f2 | 414736f1 | \([0, 1, 0, -5814944, -1382212364]\) | \(304821217/164864\) | \(11760912986165617885184\) | \([2]\) | \(24330240\) | \(2.9259\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736.f have rank \(0\).
Complex multiplication
The elliptic curves in class 414736.f do not have complex multiplication.Modular form 414736.2.a.f
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.