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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 95370.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95370.o1 | 95370p4 | \([1, 1, 0, -63685057, -194144442611]\) | \(1183430669265454849849/10449720703125000\) | \(252230854502408203125000\) | \([2]\) | \(19906560\) | \(3.3139\) | |
| 95370.o2 | 95370p3 | \([1, 1, 0, -6890777, 1988923941]\) | \(1499114720492202169/796539777000000\) | \(19226533828582113000000\) | \([2]\) | \(9953280\) | \(2.9673\) | |
| 95370.o3 | 95370p2 | \([1, 1, 0, -5461672, 4751990806]\) | \(746461053445307689/27443694341250\) | \(662424065776831421250\) | \([2]\) | \(6635520\) | \(2.7646\) | |
| 95370.o4 | 95370p1 | \([1, 1, 0, -5412542, 4844482944]\) | \(726497538898787209/1038579300\) | \(25068779515721700\) | \([2]\) | \(3317760\) | \(2.4180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.o have rank \(0\).
Complex multiplication
The elliptic curves in class 95370.o do not have complex multiplication.Modular form 95370.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
