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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 200277.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200277.l1 | 200277m2 | \([1, -1, 1, -553634, -158397500]\) | \(5861208627/847\) | \(2711986147609893\) | \([2]\) | \(1531904\) | \(1.9765\) | |
200277.l2 | 200277m1 | \([1, -1, 1, -37769, -1987232]\) | \(1860867/539\) | \(1725809366660841\) | \([2]\) | \(765952\) | \(1.6299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 200277.l have rank \(1\).
Complex multiplication
The elliptic curves in class 200277.l do not have complex multiplication.Modular form 200277.2.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.