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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5950f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5950.b2 | 5950f1 | \([1, 0, 1, -451, -3702]\) | \(647214625/3332\) | \(52062500\) | \([2]\) | \(2304\) | \(0.32654\) | \(\Gamma_0(N)\)-optimal |
5950.b1 | 5950f2 | \([1, 0, 1, -701, 798]\) | \(2433138625/1387778\) | \(21684031250\) | \([2]\) | \(4608\) | \(0.67312\) |
Rank
sage: E.rank()
The elliptic curves in class 5950f have rank \(1\).
Complex multiplication
The elliptic curves in class 5950f do not have complex multiplication.Modular form 5950.2.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.