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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 96192u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96192.o2 | 96192u1 | \([0, 0, 0, -29100, -2364208]\) | \(-14260515625/4382748\) | \(-837556185858048\) | \([2]\) | \(294912\) | \(1.5771\) | \(\Gamma_0(N)\)-optimal |
96192.o1 | 96192u2 | \([0, 0, 0, -495660, -134307376]\) | \(70470585447625/4518018\) | \(863406685421568\) | \([2]\) | \(589824\) | \(1.9237\) |
Rank
sage: E.rank()
The elliptic curves in class 96192u have rank \(0\).
Complex multiplication
The elliptic curves in class 96192u do not have complex multiplication.Modular form 96192.2.a.u
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.