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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 22800db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.cb3 | 22800db1 | \([0, 1, 0, -3208, -6412]\) | \(57066625/32832\) | \(2101248000000\) | \([2]\) | \(41472\) | \(1.0541\) | \(\Gamma_0(N)\)-optimal |
| 22800.cb4 | 22800db2 | \([0, 1, 0, 12792, -38412]\) | \(3616805375/2105352\) | \(-134742528000000\) | \([2]\) | \(82944\) | \(1.4006\) | |
| 22800.cb1 | 22800db3 | \([0, 1, 0, -171208, 27209588]\) | \(8671983378625/82308\) | \(5267712000000\) | \([2]\) | \(124416\) | \(1.6034\) | |
| 22800.cb2 | 22800db4 | \([0, 1, 0, -167208, 28545588]\) | \(-8078253774625/846825858\) | \(-54196854912000000\) | \([2]\) | \(248832\) | \(1.9499\) |
Rank
sage: E.rank()
The elliptic curves in class 22800db have rank \(1\).
Complex multiplication
The elliptic curves in class 22800db do not have complex multiplication.Modular form 22800.2.a.db
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
