Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 37026.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.o1 | 37026j4 | \([1, -1, 0, -1727487801, 27636140011189]\) | \(441453577446719855661097/4354701912\) | \(5623958033891056728\) | \([2]\) | \(10321920\) | \(3.6296\) | |
37026.o2 | 37026j2 | \([1, -1, 0, -107970561, 431813317117]\) | \(107784459654566688937/10704361149504\) | \(13824339553192436237376\) | \([2, 2]\) | \(5160960\) | \(3.2830\) | |
37026.o3 | 37026j3 | \([1, -1, 0, -99824841, 499707893317]\) | \(-85183593440646799657/34223681512621656\) | \(-44198788454808337939736664\) | \([2]\) | \(10321920\) | \(3.6296\) | |
37026.o4 | 37026j1 | \([1, -1, 0, -7259841, 5665976509]\) | \(32765849647039657/8229948198912\) | \(10628714485424088649728\) | \([2]\) | \(2580480\) | \(2.9364\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37026.o have rank \(1\).
Complex multiplication
The elliptic curves in class 37026.o do not have complex multiplication.Modular form 37026.2.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 LMFDB 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 LMFDB labels.