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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 134640.ef
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.ef1 | 134640dd2 | \([0, 0, 0, -5547, -158886]\) | \(170676802323/158950\) | \(17578598400\) | \([2]\) | \(147456\) | \(0.88862\) | |
134640.ef2 | 134640dd1 | \([0, 0, 0, -267, -3654]\) | \(-19034163/41140\) | \(-4549754880\) | \([2]\) | \(73728\) | \(0.54204\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134640.ef have rank \(1\).
Complex multiplication
The elliptic curves in class 134640.ef do not have complex multiplication.Modular form 134640.2.a.ef
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.