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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 9702.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.t1 | 9702o2 | \([1, -1, 0, -25146, 607662]\) | \(59776471/29282\) | \(861411419406846\) | \([2]\) | \(43008\) | \(1.5591\) | |
9702.t2 | 9702o1 | \([1, -1, 0, 5724, 70524]\) | \(704969/484\) | \(-14238205279452\) | \([2]\) | \(21504\) | \(1.2125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.t have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.t do not have complex multiplication.Modular form 9702.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.