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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 215600.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.l1 | 215600l2 | \([0, 1, 0, -25588208, -49828882412]\) | \(1968634623437/5929\) | \(5580327368000000000\) | \([2]\) | \(12779520\) | \(2.8250\) | |
215600.l2 | 215600l1 | \([0, 1, 0, -1578208, -800462412]\) | \(-461889917/26411\) | \(-24857821912000000000\) | \([2]\) | \(6389760\) | \(2.4784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215600.l have rank \(0\).
Complex multiplication
The elliptic curves in class 215600.l do not have complex multiplication.Modular form 215600.2.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.