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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 22320.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22320.f1 | 22320bj2 | \([0, 0, 0, -5391723, 4495296922]\) | \(5805223604235668521/435937500000000\) | \(1301702400000000000000\) | \([2]\) | \(1032192\) | \(2.7968\) | |
22320.f2 | 22320bj1 | \([0, 0, 0, 322197, 311564698]\) | \(1238798620042199/14760960000000\) | \(-44075990384640000000\) | \([2]\) | \(516096\) | \(2.4503\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22320.f have rank \(1\).
Complex multiplication
The elliptic curves in class 22320.f do not have complex multiplication.Modular form 22320.2.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.