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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 66270l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66270.m2 | 66270l1 | \([1, 0, 1, 2775562, 1262974088]\) | \(219376239860231/190857600000\) | \(-2057295167576150400000\) | \([2]\) | \(5299200\) | \(2.7772\) | \(\Gamma_0(N)\)-optimal |
66270.m1 | 66270l2 | \([1, 0, 1, -13836118, 11190114056]\) | \(27175609354259449/10707187500000\) | \(115415079630477187500000\) | \([2]\) | \(10598400\) | \(3.1237\) |
Rank
sage: E.rank()
The elliptic curves in class 66270l have rank \(0\).
Complex multiplication
The elliptic curves in class 66270l do not have complex multiplication.Modular form 66270.2.a.l
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 Cremona 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 Cremona labels.