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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 10608g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10608.t2 | 10608g1 | \([0, 1, 0, -132668, 18555180]\) | \(1008754689437602000/67254057\) | \(17217038592\) | \([2]\) | \(24576\) | \(1.4207\) | \(\Gamma_0(N)\)-optimal |
10608.t1 | 10608g2 | \([0, 1, 0, -132928, 18478532]\) | \(253674278705546500/2058765672717\) | \(2108176048862208\) | \([2]\) | \(49152\) | \(1.7673\) |
Rank
sage: E.rank()
The elliptic curves in class 10608g have rank \(1\).
Complex multiplication
The elliptic curves in class 10608g do not have complex multiplication.Modular form 10608.2.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 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.