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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 26640bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26640.bd3 | 26640bv1 | \([0, 0, 0, -28099947, 57333221786]\) | \(821774646379511057449/38361600000\) | \(114547123814400000\) | \([2]\) | \(1105920\) | \(2.7521\) | \(\Gamma_0(N)\)-optimal |
| 26640.bd2 | 26640bv2 | \([0, 0, 0, -28146027, 57135750554]\) | \(825824067562227826729/5613755625000000\) | \(16762584476160000000000\) | \([2, 2]\) | \(2211840\) | \(3.0987\) | |
| 26640.bd4 | 26640bv3 | \([0, 0, 0, -10883307, 126473191706]\) | \(-47744008200656797609/2286529541015625000\) | \(-6827540625000000000000000\) | \([2]\) | \(4423680\) | \(3.4452\) | |
| 26640.bd1 | 26640bv4 | \([0, 0, 0, -46146027, -24839849446]\) | \(3639478711331685826729/2016912141902025000\) | \(6022467385125176217600000\) | \([2]\) | \(4423680\) | \(3.4452\) |
Rank
sage: E.rank()
The elliptic curves in class 26640bv have rank \(0\).
Complex multiplication
The elliptic curves in class 26640bv do not have complex multiplication.Modular form 26640.2.a.bv
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.
