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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 64974f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64974.l1 | 64974f1 | \([1, 1, 0, -639174694, -6220081356908]\) | \(245467607504992533120574297/1733763438231552\) | \(203975534744503861248\) | \([2]\) | \(16773120\) | \(3.4950\) | \(\Gamma_0(N)\)-optimal |
| 64974.l2 | 64974f2 | \([1, 1, 0, -638767014, -6228411645420]\) | \(-244998212735457942818233177/652408656229361356416\) | \(-76755225996728134220985984\) | \([2]\) | \(33546240\) | \(3.8416\) |
Rank
sage: E.rank()
The elliptic curves in class 64974f have rank \(1\).
Complex multiplication
The elliptic curves in class 64974f do not have complex multiplication.Modular form 64974.2.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.
