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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 271950bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271950.bh4 | 271950bh1 | \([1, 1, 0, 97975, -9556875]\) | \(56578878719/54390000\) | \(-99983267343750000\) | \([2]\) | \(2949120\) | \(1.9491\) | \(\Gamma_0(N)\)-optimal |
| 271950.bh3 | 271950bh2 | \([1, 1, 0, -514525, -87344375]\) | \(8194759433281/2958272100\) | \(5438089910826562500\) | \([2, 2]\) | \(5898240\) | \(2.2956\) | |
| 271950.bh2 | 271950bh3 | \([1, 1, 0, -3515775, 2472721875]\) | \(2614441086442081/74385450090\) | \(136740215900600156250\) | \([2]\) | \(11796480\) | \(2.6422\) | |
| 271950.bh1 | 271950bh4 | \([1, 1, 0, -7313275, -7613560625]\) | \(23531588875176481/6398929110\) | \(11762931419724843750\) | \([2]\) | \(11796480\) | \(2.6422\) |
Rank
sage: E.rank()
The elliptic curves in class 271950bh have rank \(0\).
Complex multiplication
The elliptic curves in class 271950bh do not have complex multiplication.Modular form 271950.2.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.
