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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 288990dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 288990.dn4 | 288990dn1 | \([1, -1, 0, 18981, 872613]\) | \(214921799/218880\) | \(-770182634407680\) | \([2]\) | \(1966080\) | \(1.5433\) | \(\Gamma_0(N)\)-optimal |
| 288990.dn3 | 288990dn2 | \([1, -1, 0, -102699, 8100405]\) | \(34043726521/11696400\) | \(41156634526160400\) | \([2, 2]\) | \(3932160\) | \(1.8899\) | |
| 288990.dn1 | 288990dn3 | \([1, -1, 0, -1471599, 687348585]\) | \(100162392144121/23457780\) | \(82541917021910580\) | \([2]\) | \(7864320\) | \(2.2365\) | |
| 288990.dn2 | 288990dn4 | \([1, -1, 0, -680679, -210029247]\) | \(9912050027641/311647500\) | \(1096607696256247500\) | \([2]\) | \(7864320\) | \(2.2365\) |
Rank
sage: E.rank()
The elliptic curves in class 288990dn have rank \(0\).
Complex multiplication
The elliptic curves in class 288990dn do not have complex multiplication.Modular form 288990.2.a.dn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
