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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 28611.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28611.r1 | 28611r2 | \([0, 0, 1, -258366, 115628683]\) | \(-108394872832/265513259\) | \(-4672047720345453459\) | \([]\) | \(414720\) | \(2.2704\) | |
28611.r2 | 28611r1 | \([0, 0, 1, 27744, -3536132]\) | \(134217728/384659\) | \(-6768570469244859\) | \([]\) | \(138240\) | \(1.7211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28611.r have rank \(1\).
Complex multiplication
The elliptic curves in class 28611.r do not have complex multiplication.Modular form 28611.2.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.