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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 40656br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.w4 | 40656br1 | \([0, -1, 0, 807, -3276]\) | \(2048000/1323\) | \(-37500403248\) | \([2]\) | \(25920\) | \(0.71788\) | \(\Gamma_0(N)\)-optimal |
| 40656.w3 | 40656br2 | \([0, -1, 0, -3428, -23604]\) | \(9826000/5103\) | \(2314310600448\) | \([2]\) | \(51840\) | \(1.0645\) | |
| 40656.w2 | 40656br3 | \([0, -1, 0, -13713, -631992]\) | \(-10061824000/352947\) | \(-10004274244272\) | \([2]\) | \(77760\) | \(1.2672\) | |
| 40656.w1 | 40656br4 | \([0, -1, 0, -221228, -39976836]\) | \(2640279346000/3087\) | \(1400015054592\) | \([2]\) | \(155520\) | \(1.6138\) |
Rank
sage: E.rank()
The elliptic curves in class 40656br have rank \(0\).
Complex multiplication
The elliptic curves in class 40656br do not have complex multiplication.Modular form 40656.2.a.br
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.
