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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 79560.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79560.u1 | 79560bk4 | \([0, 0, 0, -2291403, 1335058598]\) | \(891190736491222802/3729375\) | \(5567927040000\) | \([2]\) | \(983040\) | \(2.0772\) | |
79560.u2 | 79560bk2 | \([0, 0, 0, -143283, 20838782]\) | \(435792975088324/890127225\) | \(664476412953600\) | \([2, 2]\) | \(491520\) | \(1.7306\) | |
79560.u3 | 79560bk3 | \([0, 0, 0, -94683, 35195222]\) | \(-62875617222962/322034842935\) | \(-480795444223211520\) | \([2]\) | \(983040\) | \(2.0772\) | |
79560.u4 | 79560bk1 | \([0, 0, 0, -12063, 79778]\) | \(1040212820176/587242305\) | \(109593507928320\) | \([2]\) | \(245760\) | \(1.3840\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79560.u have rank \(0\).
Complex multiplication
The elliptic curves in class 79560.u do not have complex multiplication.Modular form 79560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.