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SageMath
E = EllipticCurve("mb1")
E.isogeny_class()
Elliptic curves in class 235200mb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.mb3 | 235200mb1 | \([0, -1, 0, -6492908, -5935305438]\) | \(257307998572864/19456203375\) | \(2289002870865375000000\) | \([2]\) | \(10616832\) | \(2.8437\) | \(\Gamma_0(N)\)-optimal |
| 235200.mb2 | 235200mb2 | \([0, -1, 0, -21199033, 30580002937]\) | \(139927692143296/27348890625\) | \(205924456521000000000000\) | \([2, 2]\) | \(21233664\) | \(3.1902\) | |
| 235200.mb1 | 235200mb3 | \([0, -1, 0, -321324033, 2216990627937]\) | \(60910917333827912/3255076125\) | \(196073702927424000000000\) | \([2]\) | \(42467328\) | \(3.5368\) | |
| 235200.mb4 | 235200mb4 | \([0, -1, 0, 43627967, 180913815937]\) | \(152461584507448/322998046875\) | \(-19456203375000000000000000\) | \([2]\) | \(42467328\) | \(3.5368\) |
Rank
sage: E.rank()
The elliptic curves in class 235200mb have rank \(1\).
Complex multiplication
The elliptic curves in class 235200mb do not have complex multiplication.Modular form 235200.2.a.mb
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.
