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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 9702m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.o2 | 9702m1 | \([1, -1, 0, -34407, 1598589]\) | \(1071912625/360448\) | \(1514797112328192\) | \([]\) | \(50400\) | \(1.6153\) | \(\Gamma_0(N)\)-optimal |
9702.o1 | 9702m2 | \([1, -1, 0, -2504007, 1525736925]\) | \(413160293352625/42592\) | \(178994580655968\) | \([3]\) | \(151200\) | \(2.1646\) |
Rank
sage: E.rank()
The elliptic curves in class 9702m have rank \(1\).
Complex multiplication
The elliptic curves in class 9702m do not have complex multiplication.Modular form 9702.2.a.m
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.