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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 102960.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.u1 | 102960bd2 | \([0, 0, 0, -154599483, -739878085222]\) | \(547419594877749407409124/8035865921655\) | \(5998741767051770880\) | \([2]\) | \(9011200\) | \(3.1546\) | |
102960.u2 | 102960bd1 | \([0, 0, 0, -9653583, -11582916082]\) | \(-533116130640227974096/2048408107863975\) | \(-382282114722006470400\) | \([2]\) | \(4505600\) | \(2.8080\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.u have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.u do not have complex multiplication.Modular form 102960.2.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 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.