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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 41328.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41328.bj1 | 41328bi2 | \([0, 0, 0, -1384029027, -19818277784478]\) | \(98191033604529537629349729/10906239337336\) | \(32565856161455898624\) | \([]\) | \(8297856\) | \(3.6132\) | |
41328.bj2 | 41328bi1 | \([0, 0, 0, -2786787, 1648296162]\) | \(801581275315909089/70810888830976\) | \(211440181075073040384\) | \([]\) | \(1185408\) | \(2.6402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41328.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 41328.bj do not have complex multiplication.Modular form 41328.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.