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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1870.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1870.h1 | 1870h1 | \([1, 1, 1, -2439835, 1467522537]\) | \(-1606220241149825308027441/2128704136908800000\) | \(-2128704136908800000\) | \([5]\) | \(48000\) | \(2.4232\) | \(\Gamma_0(N)\)-optimal |
| 1870.h2 | 1870h2 | \([1, 1, 1, 17283565, -17141361543]\) | \(570983676137286216962798159/457469996554140806256680\) | \(-457469996554140806256680\) | \([]\) | \(240000\) | \(3.2279\) |
Rank
sage: E.rank()
The elliptic curves in class 1870.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1870.h do not have complex multiplication.Modular form 1870.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
