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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 102550g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102550.q2 | 102550g1 | \([1, -1, 0, 239708, 291889616]\) | \(97487796040631919/2412980990000000\) | \(-37702827968750000000\) | \([]\) | \(9483264\) | \(2.4365\) | \(\Gamma_0(N)\)-optimal |
102550.q1 | 102550g2 | \([1, -1, 0, -138649042, -628720244134]\) | \(-18864891308791949569351281/12976912684820654990\) | \(-202764260700322734218750\) | \([]\) | \(66382848\) | \(3.4095\) |
Rank
sage: E.rank()
The elliptic curves in class 102550g have rank \(0\).
Complex multiplication
The elliptic curves in class 102550g do not have complex multiplication.Modular form 102550.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.