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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 235950f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.f2 | 235950f1 | \([1, 1, 0, 1450, 458220]\) | \(7604375/2047032\) | \(-90661051423800\) | \([]\) | \(933120\) | \(1.3574\) | \(\Gamma_0(N)\)-optimal |
235950.f1 | 235950f2 | \([1, 1, 0, -406925, 99758685]\) | \(-168256703745625/30371328\) | \(-1345116505075200\) | \([]\) | \(2799360\) | \(1.9067\) |
Rank
sage: E.rank()
The elliptic curves in class 235950f have rank \(1\).
Complex multiplication
The elliptic curves in class 235950f do not have complex multiplication.Modular form 235950.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.