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SageMath
E = EllipticCurve("jn1")
E.isogeny_class()
Elliptic curves in class 705600.jn
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.jn1 | \([0, 0, 0, -346464300, 2482293058000]\) | \(-5452947409/250\) | \(-210866643477504000000000\) | \([]\) | \(139345920\) | \(3.5511\) |
705600.jn2 | \([0, 0, 0, -720300, 8840482000]\) | \(-49/40\) | \(-33738662956400640000000\) | \([]\) | \(46448640\) | \(3.0018\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.jn have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.jn do not have complex multiplication.Modular form 705600.2.a.jn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.