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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 52983.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52983.h1 | 52983d2 | \([1, -1, 0, -1169568, -486546345]\) | \(408023180713/1421\) | \(616182831633789\) | \([2]\) | \(483840\) | \(2.0573\) | |
| 52983.h2 | 52983d1 | \([1, -1, 0, -72063, -7814664]\) | \(-95443993/5887\) | \(-2552757445339983\) | \([2]\) | \(241920\) | \(1.7107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52983.h have rank \(1\).
Complex multiplication
The elliptic curves in class 52983.h do not have complex multiplication.Modular form 52983.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
