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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 59200.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59200.u1 | 59200be1 | \([0, 1, 0, -85633, 9616863]\) | \(-16954786009/370\) | \(-1515520000000\) | \([]\) | \(165888\) | \(1.4532\) | \(\Gamma_0(N)\)-optimal |
| 59200.u2 | 59200be2 | \([0, 1, 0, -29633, 21992863]\) | \(-702595369/50653000\) | \(-207474688000000000\) | \([]\) | \(497664\) | \(2.0025\) | |
| 59200.u3 | 59200be3 | \([0, 1, 0, 266367, -589839137]\) | \(510273943271/37000000000\) | \(-151552000000000000000\) | \([]\) | \(1492992\) | \(2.5518\) |
Rank
sage: E.rank()
The elliptic curves in class 59200.u have rank \(2\).
Complex multiplication
The elliptic curves in class 59200.u do not have complex multiplication.Modular form 59200.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
