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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2790.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2790.h1 | 2790h2 | \([1, -1, 0, -9594, 364108]\) | \(133974081659809/192200\) | \(140113800\) | \([2]\) | \(2304\) | \(0.83425\) | |
| 2790.h2 | 2790h1 | \([1, -1, 0, -594, 5908]\) | \(-31824875809/1240000\) | \(-903960000\) | \([2]\) | \(1152\) | \(0.48767\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2790.h have rank \(1\).
Complex multiplication
The elliptic curves in class 2790.h do not have complex multiplication.Modular form 2790.2.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.
