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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 13860.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13860.g1 | 13860b2 | \([0, 0, 0, -8343, 210222]\) | \(12745567728/3587045\) | \(18074574524160\) | \([2]\) | \(32256\) | \(1.2508\) | |
13860.g2 | 13860b1 | \([0, 0, 0, -7668, 258417]\) | \(158328373248/21175\) | \(6668600400\) | \([2]\) | \(16128\) | \(0.90419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.g have rank \(1\).
Complex multiplication
The elliptic curves in class 13860.g do not have complex multiplication.Modular form 13860.2.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.