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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 18490.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18490.i1 | 18490g2 | \([1, -1, 1, -1723, -26669]\) | \(7111117467/125000\) | \(9938375000\) | \([2]\) | \(11088\) | \(0.71469\) | |
18490.i2 | 18490g1 | \([1, -1, 1, -3, -1213]\) | \(-27/8000\) | \(-636056000\) | \([2]\) | \(5544\) | \(0.36812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18490.i have rank \(0\).
Complex multiplication
The elliptic curves in class 18490.i do not have complex multiplication.Modular form 18490.2.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.