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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7406.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7406.f1 | 7406i2 | \([1, 0, 0, -92057, -10745063]\) | \(582810602977/829472\) | \(122791624920608\) | \([2]\) | \(42240\) | \(1.6064\) | |
7406.f2 | 7406i1 | \([1, 0, 0, -7417, -63495]\) | \(304821217/164864\) | \(24405788804096\) | \([2]\) | \(21120\) | \(1.2598\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7406.f have rank \(0\).
Complex multiplication
The elliptic curves in class 7406.f do not have complex multiplication.Modular form 7406.2.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.