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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 22542.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22542.o1 | 22542m4 | \([1, 0, 1, -315450, 68164816]\) | \(143820170742457/5826444\) | \(140636194074636\) | \([2]\) | \(147456\) | \(1.7971\) | |
22542.o2 | 22542m3 | \([1, 0, 1, -95810, -10526416]\) | \(4029546653497/351790452\) | \(8491366308691188\) | \([2]\) | \(147456\) | \(1.7971\) | |
22542.o3 | 22542m2 | \([1, 0, 1, -20670, 954976]\) | \(40459583737/7033104\) | \(169762033084176\) | \([2, 2]\) | \(73728\) | \(1.4505\) | |
22542.o4 | 22542m1 | \([1, 0, 1, 2450, 85664]\) | \(67419143/169728\) | \(-4096821311232\) | \([2]\) | \(36864\) | \(1.1039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22542.o have rank \(1\).
Complex multiplication
The elliptic curves in class 22542.o do not have complex multiplication.Modular form 22542.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.