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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 333795a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333795.a2 | 333795a1 | \([0, -1, 1, -2583756, 1872892712]\) | \(-79028701534867456/16987307596875\) | \(-410032309243794496875\) | \([]\) | \(26400000\) | \(2.6764\) | \(\Gamma_0(N)\)-optimal |
333795.a1 | 333795a2 | \([0, -1, 1, -7742406, -156763848628]\) | \(-2126464142970105856/438611057788643355\) | \(-10587004671536366397703995\) | \([]\) | \(132000000\) | \(3.4811\) |
Rank
sage: E.rank()
The elliptic curves in class 333795a have rank \(1\).
Complex multiplication
The elliptic curves in class 333795a do not have complex multiplication.Modular form 333795.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.