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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 258570.fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 258570.fh1 | 258570fh1 | \([1, -1, 1, -20716052, -35872861449]\) | \(279419703685750081/3666124800000\) | \(12900153767047372800000\) | \([2]\) | \(20643840\) | \(3.0503\) | \(\Gamma_0(N)\)-optimal |
| 258570.fh2 | 258570fh2 | \([1, -1, 1, -3194132, -94634372361]\) | \(-1024222994222401/1098922500000000\) | \(-3866826690697522500000000\) | \([2]\) | \(41287680\) | \(3.3969\) |
Rank
sage: E.rank()
The elliptic curves in class 258570.fh have rank \(1\).
Complex multiplication
The elliptic curves in class 258570.fh do not have complex multiplication.Modular form 258570.2.a.fh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
