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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 236992.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.l1 | 236992l2 | \([0, 1, 0, -136129, 9046527]\) | \(57512456/25921\) | \(125738623918702592\) | \([2]\) | \(2433024\) | \(1.9763\) | |
236992.l2 | 236992l1 | \([0, 1, 0, -114969, 14958631]\) | \(277167808/161\) | \(97623155216384\) | \([2]\) | \(1216512\) | \(1.6298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.l have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.l do not have complex multiplication.Modular form 236992.2.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.