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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 169065.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169065.l1 | 169065l2 | \([1, -1, 1, -1038287, 407469124]\) | \(260549802603/4225\) | \(2007296530899075\) | \([2]\) | \(1892352\) | \(2.0687\) | |
169065.l2 | 169065l1 | \([1, -1, 1, -62912, 6785074]\) | \(-57960603/8125\) | \(-3860185636344375\) | \([2]\) | \(946176\) | \(1.7221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 169065.l have rank \(0\).
Complex multiplication
The elliptic curves in class 169065.l do not have complex multiplication.Modular form 169065.2.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 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.