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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 2880.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.bh1 | 2880bf4 | \([0, 0, 0, -17292, 875216]\) | \(23937672968/45\) | \(1074954240\) | \([2]\) | \(4096\) | \(0.98820\) | |
| 2880.bh2 | 2880bf3 | \([0, 0, 0, -2892, -42064]\) | \(111980168/32805\) | \(783641640960\) | \([2]\) | \(4096\) | \(0.98820\) | |
| 2880.bh3 | 2880bf2 | \([0, 0, 0, -1092, 13376]\) | \(48228544/2025\) | \(6046617600\) | \([2, 2]\) | \(2048\) | \(0.64163\) | |
| 2880.bh4 | 2880bf1 | \([0, 0, 0, 33, 776]\) | \(85184/5625\) | \(-262440000\) | \([2]\) | \(1024\) | \(0.29505\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2880.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 2880.bh do not have complex multiplication.Modular form 2880.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
