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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 27930.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27930.r1 | 27930p1 | \([1, 1, 0, -519327, -253556001]\) | \(-131661708271504489/159475479581250\) | \(-18762130697254481250\) | \([]\) | \(967680\) | \(2.3919\) | \(\Gamma_0(N)\)-optimal |
27930.r2 | 27930p2 | \([1, 1, 0, 4382388, 4758786936]\) | \(79116632600119361351/128876220703125000\) | \(-15162158489501953125000\) | \([]\) | \(2903040\) | \(2.9412\) |
Rank
sage: E.rank()
The elliptic curves in class 27930.r have rank \(1\).
Complex multiplication
The elliptic curves in class 27930.r do not have complex multiplication.Modular form 27930.2.a.r
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 LMFDB 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 LMFDB labels.