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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2800o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2800.m4 | 2800o1 | \([0, 0, 0, 925, 17250]\) | \(1367631/2800\) | \(-179200000000\) | \([2]\) | \(2304\) | \(0.84371\) | \(\Gamma_0(N)\)-optimal |
| 2800.m3 | 2800o2 | \([0, 0, 0, -7075, 185250]\) | \(611960049/122500\) | \(7840000000000\) | \([2, 2]\) | \(4608\) | \(1.1903\) | |
| 2800.m2 | 2800o3 | \([0, 0, 0, -35075, -2362750]\) | \(74565301329/5468750\) | \(350000000000000\) | \([2]\) | \(9216\) | \(1.5369\) | |
| 2800.m1 | 2800o4 | \([0, 0, 0, -107075, 13485250]\) | \(2121328796049/120050\) | \(7683200000000\) | \([2]\) | \(9216\) | \(1.5369\) |
Rank
sage: E.rank()
The elliptic curves in class 2800o have rank \(0\).
Complex multiplication
The elliptic curves in class 2800o do not have complex multiplication.Modular form 2800.2.a.o
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.
