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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2415.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2415.h1 | 2415e3 | \([1, 0, 1, -4294, 107927]\) | \(8753151307882969/65205\) | \(65205\) | \([2]\) | \(1408\) | \(0.51833\) | |
| 2415.h2 | 2415e2 | \([1, 0, 1, -269, 1667]\) | \(2141202151369/5832225\) | \(5832225\) | \([2, 2]\) | \(704\) | \(0.17176\) | |
| 2415.h3 | 2415e4 | \([1, 0, 1, -164, 3011]\) | \(-483551781049/3672913125\) | \(-3672913125\) | \([2]\) | \(1408\) | \(0.51833\) | |
| 2415.h4 | 2415e1 | \([1, 0, 1, -24, 1]\) | \(1439069689/828345\) | \(828345\) | \([2]\) | \(352\) | \(-0.17481\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2415.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2415.h do not have complex multiplication.Modular form 2415.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
