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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 167214.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
167214.r1 | 167214e2 | \([1, 1, 1, -6257091, 6039317967]\) | \(-30526075007211889/103499257854\) | \(-91855972326193160574\) | \([]\) | \(5927040\) | \(2.6946\) | |
167214.r2 | 167214e1 | \([1, 1, 1, -981, -4084293]\) | \(-117649/8118144\) | \(-7204882682888064\) | \([]\) | \(846720\) | \(1.7217\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 167214.r have rank \(1\).
Complex multiplication
The elliptic curves in class 167214.r do not have complex multiplication.Modular form 167214.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.