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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 111090.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.g1 | 111090g2 | \([1, 1, 0, -8578, -242018]\) | \(5738223173327/1302030450\) | \(15841804485150\) | \([2]\) | \(442368\) | \(1.2455\) | |
111090.g2 | 111090g1 | \([1, 1, 0, -2828, 53532]\) | \(205692449327/12757500\) | \(155220502500\) | \([2]\) | \(221184\) | \(0.89890\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 111090.g have rank \(1\).
Complex multiplication
The elliptic curves in class 111090.g do not have complex multiplication.Modular form 111090.2.a.g
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.