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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 90354f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90354.a2 | 90354f1 | \([1, 1, 0, -165677, -91163235]\) | \(-3869893/25344\) | \(-3293750333366431488\) | \([2]\) | \(3921408\) | \(2.2366\) | \(\Gamma_0(N)\)-optimal |
90354.a1 | 90354f2 | \([1, 1, 0, -4217917, -3328902995]\) | \(63856107973/156816\) | \(20380080187704794832\) | \([2]\) | \(7842816\) | \(2.5832\) |
Rank
sage: E.rank()
The elliptic curves in class 90354f have rank \(1\).
Complex multiplication
The elliptic curves in class 90354f do not have complex multiplication.Modular form 90354.2.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 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.