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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 58080bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58080.e3 | 58080bh1 | \([0, -1, 0, -766, 3016]\) | \(438976/225\) | \(25510478400\) | \([2, 2]\) | \(40960\) | \(0.68911\) | \(\Gamma_0(N)\)-optimal |
| 58080.e4 | 58080bh2 | \([0, -1, 0, 2864, 20440]\) | \(2863288/1875\) | \(-1700698560000\) | \([2]\) | \(81920\) | \(1.0357\) | |
| 58080.e2 | 58080bh3 | \([0, -1, 0, -6816, -212364]\) | \(38614472/405\) | \(367350888960\) | \([2]\) | \(81920\) | \(1.0357\) | |
| 58080.e1 | 58080bh4 | \([0, -1, 0, -9841, 378721]\) | \(14526784/15\) | \(108844707840\) | \([2]\) | \(81920\) | \(1.0357\) |
Rank
sage: E.rank()
The elliptic curves in class 58080bh have rank \(1\).
Complex multiplication
The elliptic curves in class 58080bh do not have complex multiplication.Modular form 58080.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
