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SageMath
E = EllipticCurve("ma1")
E.isogeny_class()
Elliptic curves in class 235200.ma
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.ma1 | 235200ma4 | \([0, -1, 0, -2432033, -811896063]\) | \(26410345352/10546875\) | \(635304600000000000000\) | \([2]\) | \(10616832\) | \(2.6899\) | |
| 235200.ma2 | 235200ma2 | \([0, -1, 0, -1109033, 440984937]\) | \(20034997696/455625\) | \(3430644840000000000\) | \([2, 2]\) | \(5308416\) | \(2.3433\) | |
| 235200.ma3 | 235200ma1 | \([0, -1, 0, -1102908, 446185062]\) | \(1261112198464/675\) | \(79413075000000\) | \([2]\) | \(2654208\) | \(1.9967\) | \(\Gamma_0(N)\)-optimal |
| 235200.ma4 | 235200ma3 | \([0, -1, 0, 115967, 1360959937]\) | \(2863288/13286025\) | \(-800300828275200000000\) | \([2]\) | \(10616832\) | \(2.6899\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.ma have rank \(2\).
Complex multiplication
The elliptic curves in class 235200.ma do not have complex multiplication.Modular form 235200.2.a.ma
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
