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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 92400fa
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.f1 | 92400fa1 | \([0, -1, 0, -33208, -11155088]\) | \(-2531307865/32199552\) | \(-51519283200000000\) | \([]\) | \(725760\) | \(1.8884\) | \(\Gamma_0(N)\)-optimal |
92400.f2 | 92400fa2 | \([0, -1, 0, 296792, 289804912]\) | \(1807002849335/23737663488\) | \(-37980261580800000000\) | \([]\) | \(2177280\) | \(2.4378\) |
Rank
sage: E.rank()
The elliptic curves in class 92400fa have rank \(1\).
Complex multiplication
The elliptic curves in class 92400fa do not have complex multiplication.Modular form 92400.2.a.fa
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.