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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7497f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7497.j2 | 7497f1 | \([0, 0, 1, 294, -9347]\) | \(32768/459\) | \(-39366649539\) | \([]\) | \(4608\) | \(0.71373\) | \(\Gamma_0(N)\)-optimal |
7497.j1 | 7497f2 | \([0, 0, 1, -26166, -1630022]\) | \(-23100424192/14739\) | \(-1264106857419\) | \([]\) | \(13824\) | \(1.2630\) |
Rank
sage: E.rank()
The elliptic curves in class 7497f have rank \(1\).
Complex multiplication
The elliptic curves in class 7497f do not have complex multiplication.Modular form 7497.2.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.