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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 249090e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.e2 | 249090e1 | \([1, 1, 0, 48367, 4239573]\) | \(265971760991/317400000\) | \(-14932362629400000\) | \([2]\) | \(1658880\) | \(1.7897\) | \(\Gamma_0(N)\)-optimal |
249090.e1 | 249090e2 | \([1, 1, 0, -283753, 40174957]\) | \(53706380371489/16171875000\) | \(760820106796875000\) | \([2]\) | \(3317760\) | \(2.1363\) |
Rank
sage: E.rank()
The elliptic curves in class 249090e have rank \(1\).
Complex multiplication
The elliptic curves in class 249090e do not have complex multiplication.Modular form 249090.2.a.e
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 Cremona 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 Cremona labels.