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SageMath
E = EllipticCurve("jk1")
E.isogeny_class()
Elliptic curves in class 374850jk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.jk1 | 374850jk1 | \([1, -1, 1, -15137555, 22673866947]\) | \(-4768951705/272\) | \(-21879473505356250000\) | \([]\) | \(14515200\) | \(2.7749\) | \(\Gamma_0(N)\)-optimal |
374850.jk2 | 374850jk2 | \([1, -1, 1, -1631930, 61218920697]\) | \(-5975305/20123648\) | \(-1618730967820276800000000\) | \([]\) | \(43545600\) | \(3.3242\) |
Rank
sage: E.rank()
The elliptic curves in class 374850jk have rank \(1\).
Complex multiplication
The elliptic curves in class 374850jk do not have complex multiplication.Modular form 374850.2.a.jk
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.