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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 29040.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.v1 | 29040ce4 | \([0, -1, 0, -30249556, -64026275300]\) | \(6749703004355978704/5671875\) | \(2572306572000000\) | \([2]\) | \(829440\) | \(2.6925\) | |
| 29040.v2 | 29040ce3 | \([0, -1, 0, -1890181, -1000400300]\) | \(-26348629355659264/24169921875\) | \(-685095855468750000\) | \([2]\) | \(414720\) | \(2.3459\) | |
| 29040.v3 | 29040ce2 | \([0, -1, 0, -381916, -83523284]\) | \(13584145739344/1195803675\) | \(542320423497388800\) | \([2]\) | \(276480\) | \(2.1432\) | |
| 29040.v4 | 29040ce1 | \([0, -1, 0, 26459, -6095384]\) | \(72268906496/606436875\) | \(-17189438667390000\) | \([2]\) | \(138240\) | \(1.7966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29040.v have rank \(1\).
Complex multiplication
The elliptic curves in class 29040.v do not have complex multiplication.Modular form 29040.2.a.v
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 LMFDB 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 LMFDB labels.
