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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 882.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
882.l1 | 882k2 | \([1, -1, 1, -1238, -15991]\) | \(838561807/26244\) | \(6562233468\) | \([2]\) | \(1024\) | \(0.65879\) | |
882.l2 | 882k1 | \([1, -1, 1, 22, -871]\) | \(4913/1296\) | \(-324060912\) | \([2]\) | \(512\) | \(0.31221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 882.l have rank \(0\).
Complex multiplication
The elliptic curves in class 882.l do not have complex multiplication.Modular form 882.2.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.