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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 66654bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66654.br4 | 66654bl1 | \([1, -1, 1, 22112365, 281857562291]\) | \(11079872671250375/324440155855872\) | \(-35012985649679051627461632\) | \([2]\) | \(20275200\) | \(3.5815\) | \(\Gamma_0(N)\)-optimal |
| 66654.br2 | 66654bl2 | \([1, -1, 1, -533210675, 4515418290035]\) | \(155355156733986861625/8291568305839392\) | \(894810820626826390449886752\) | \([2]\) | \(40550400\) | \(3.9281\) | |
| 66654.br3 | 66654bl3 | \([1, -1, 1, -199631210, -7743964870231]\) | \(-8152944444844179625/235342826399858688\) | \(-25397765519363422006938697728\) | \([2]\) | \(60825600\) | \(4.1308\) | |
| 66654.br1 | 66654bl4 | \([1, -1, 1, -7220011370, -234985246193239]\) | \(385693937170561837203625/2159357734550274048\) | \(233033920147415182905306021888\) | \([2]\) | \(121651200\) | \(4.4774\) |
Rank
sage: E.rank()
The elliptic curves in class 66654bl have rank \(0\).
Complex multiplication
The elliptic curves in class 66654bl do not have complex multiplication.Modular form 66654.2.a.bl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
