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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 37674f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37674.b2 | 37674f1 | \([1, -1, 0, -4194, 124564]\) | \(-11192824869409/2563305472\) | \(-1868649689088\) | \([2]\) | \(119808\) | \(1.0744\) | \(\Gamma_0(N)\)-optimal |
| 37674.b1 | 37674f2 | \([1, -1, 0, -70434, 7212244]\) | \(53008645999484449/2060047808\) | \(1501774852032\) | \([2]\) | \(239616\) | \(1.4210\) |
Rank
sage: E.rank()
The elliptic curves in class 37674f have rank \(1\).
Complex multiplication
The elliptic curves in class 37674f do not have complex multiplication.Modular form 37674.2.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.
