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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 62790b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62790.b4 | 62790b1 | \([1, 1, 0, -48468, 3156048]\) | \(12592240519595268169/2928935364526080\) | \(2928935364526080\) | \([2]\) | \(442368\) | \(1.6798\) | \(\Gamma_0(N)\)-optimal |
| 62790.b2 | 62790b2 | \([1, 1, 0, -725588, 237574992]\) | \(42246907341249375922249/3454082159673600\) | \(3454082159673600\) | \([2, 2]\) | \(884736\) | \(2.0264\) | |
| 62790.b3 | 62790b3 | \([1, 1, 0, -675908, 271566048]\) | \(-34149745884055625715529/12162716353561410000\) | \(-12162716353561410000\) | \([2]\) | \(1769472\) | \(2.3729\) | |
| 62790.b1 | 62790b4 | \([1, 1, 0, -11609188, 15219938752]\) | \(173033145740429750714040649/1156798253520\) | \(1156798253520\) | \([2]\) | \(1769472\) | \(2.3729\) |
Rank
sage: E.rank()
The elliptic curves in class 62790b have rank \(2\).
Complex multiplication
The elliptic curves in class 62790b do not have complex multiplication.Modular form 62790.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
