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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 122010g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122010.j1 | 122010g1 | \([1, 1, 0, -3707, 21981]\) | \(16431620361967/8811970560\) | \(3022505902080\) | \([2]\) | \(276480\) | \(1.0860\) | \(\Gamma_0(N)\)-optimal |
122010.j2 | 122010g2 | \([1, 1, 0, 14213, 190429]\) | \(925633609502993/578543731200\) | \(-198440499801600\) | \([2]\) | \(552960\) | \(1.4325\) |
Rank
sage: E.rank()
The elliptic curves in class 122010g have rank \(0\).
Complex multiplication
The elliptic curves in class 122010g do not have complex multiplication.Modular form 122010.2.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.