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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2790.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.j1 | 2790k2 | \([1, -1, 0, -1449, -4667]\) | \(461710681489/252204840\) | \(183857328360\) | \([2]\) | \(3072\) | \(0.85223\) | |
2790.j2 | 2790k1 | \([1, -1, 0, 351, -707]\) | \(6549699311/4017600\) | \(-2928830400\) | \([2]\) | \(1536\) | \(0.50566\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2790.j have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.j do not have complex multiplication.Modular form 2790.2.a.j
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.