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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 2790.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.p1 | 2790t2 | \([1, -1, 1, -18113, 333281]\) | \(901456690969801/457629750000\) | \(333612087750000\) | \([2]\) | \(15360\) | \(1.4792\) | |
2790.p2 | 2790t1 | \([1, -1, 1, 4207, 38657]\) | \(11298232190519/7472736000\) | \(-5447624544000\) | \([2]\) | \(7680\) | \(1.1326\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2790.p have rank \(1\).
Complex multiplication
The elliptic curves in class 2790.p do not have complex multiplication.Modular form 2790.2.a.p
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.