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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 14157f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14157.c2 | 14157f1 | \([1, -1, 1, 17764, -50950754]\) | \(17779581/32166277\) | \(-1121626343541998151\) | \([2]\) | \(172800\) | \(2.1424\) | \(\Gamma_0(N)\)-optimal |
14157.c1 | 14157f2 | \([1, -1, 1, -1958771, -1032102728]\) | \(23835655373139/584043889\) | \(20365397328609668907\) | \([2]\) | \(345600\) | \(2.4890\) |
Rank
sage: E.rank()
The elliptic curves in class 14157f have rank \(1\).
Complex multiplication
The elliptic curves in class 14157f do not have complex multiplication.Modular form 14157.2.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.