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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 96192t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96192.l2 | 96192t1 | \([0, 0, 0, 1140, 35728]\) | \(3429500/13527\) | \(-646262489088\) | \([2]\) | \(81920\) | \(0.94892\) | \(\Gamma_0(N)\)-optimal |
96192.l1 | 96192t2 | \([0, 0, 0, -11820, 434896]\) | \(1911343250/251001\) | \(23983519039488\) | \([2]\) | \(163840\) | \(1.2955\) |
Rank
sage: E.rank()
The elliptic curves in class 96192t have rank \(2\).
Complex multiplication
The elliptic curves in class 96192t do not have complex multiplication.Modular form 96192.2.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 Cremona 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 Cremona labels.