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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 11400bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11400.bh4 | 11400bh1 | \([0, 1, 0, 492, 7488]\) | \(3286064/7695\) | \(-30780000000\) | \([4]\) | \(9216\) | \(0.69652\) | \(\Gamma_0(N)\)-optimal |
| 11400.bh3 | 11400bh2 | \([0, 1, 0, -4008, 79488]\) | \(445138564/81225\) | \(1299600000000\) | \([2, 2]\) | \(18432\) | \(1.0431\) | |
| 11400.bh2 | 11400bh3 | \([0, 1, 0, -19008, -940512]\) | \(23735908082/1954815\) | \(62554080000000\) | \([2]\) | \(36864\) | \(1.3897\) | |
| 11400.bh1 | 11400bh4 | \([0, 1, 0, -61008, 5779488]\) | \(784767874322/35625\) | \(1140000000000\) | \([2]\) | \(36864\) | \(1.3897\) |
Rank
sage: E.rank()
The elliptic curves in class 11400bh have rank \(1\).
Complex multiplication
The elliptic curves in class 11400bh do not have complex multiplication.Modular form 11400.2.a.bh
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.
