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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 169338.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169338.i1 | 169338p2 | \([1, 0, 1, -1458136, 666147302]\) | \(71032527376098625/1376417195712\) | \(6643702908017443008\) | \([2]\) | \(3483648\) | \(2.4044\) | |
169338.i2 | 169338p1 | \([1, 0, 1, 2024, 30685670]\) | \(190109375/84273426432\) | \(-406771733162815488\) | \([2]\) | \(1741824\) | \(2.0578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 169338.i have rank \(1\).
Complex multiplication
The elliptic curves in class 169338.i do not have complex multiplication.Modular form 169338.2.a.i
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.