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SageMath
E = EllipticCurve("jp1")
E.isogeny_class()
Elliptic curves in class 78400jp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.bv2 | 78400jp1 | \([0, 1, 0, -628833, -161165537]\) | \(46585/8\) | \(4722524979200000000\) | \([]\) | \(1451520\) | \(2.3036\) | \(\Gamma_0(N)\)-optimal |
78400.bv1 | 78400jp2 | \([0, 1, 0, -14348833, 20899034463]\) | \(553463785/512\) | \(302241598668800000000\) | \([]\) | \(4354560\) | \(2.8529\) |
Rank
sage: E.rank()
The elliptic curves in class 78400jp have rank \(1\).
Complex multiplication
The elliptic curves in class 78400jp do not have complex multiplication.Modular form 78400.2.a.jp
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.