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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 126960.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126960.r1 | 126960bc2 | \([0, -1, 0, -1121656, 458233456]\) | \(-136154455833049/216000000\) | \(-247585406976000000\) | \([]\) | \(1492992\) | \(2.2356\) | |
126960.r2 | 126960bc1 | \([0, -1, 0, 20984, 3005680]\) | \(891449111/3936600\) | \(-4512244042137600\) | \([]\) | \(497664\) | \(1.6863\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126960.r have rank \(1\).
Complex multiplication
The elliptic curves in class 126960.r do not have complex multiplication.Modular form 126960.2.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.