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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 6080.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6080.u1 | 6080d2 | \([0, -1, 0, -1666641, -827598895]\) | \(31248575021659890256/28203125\) | \(462080000000\) | \([2]\) | \(71680\) | \(1.9691\) | |
| 6080.u2 | 6080d1 | \([0, -1, 0, -104141, -12911395]\) | \(-121981271658244096/115966796875\) | \(-118750000000000\) | \([2]\) | \(35840\) | \(1.6225\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6080.u have rank \(0\).
Complex multiplication
The elliptic curves in class 6080.u do not have complex multiplication.Modular form 6080.2.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.
