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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 25270g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25270.j2 | 25270g1 | \([1, 1, 0, 12, 8]\) | \(463391/280\) | \(-101080\) | \([]\) | \(2592\) | \(-0.35045\) | \(\Gamma_0(N)\)-optimal |
25270.j1 | 25270g2 | \([1, 1, 0, -178, 882]\) | \(-1742943169/85750\) | \(-30955750\) | \([]\) | \(7776\) | \(0.19886\) |
Rank
sage: E.rank()
The elliptic curves in class 25270g have rank \(1\).
Complex multiplication
The elliptic curves in class 25270g do not have complex multiplication.Modular form 25270.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.