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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 372810.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372810.o1 | 372810o4 | \([1, 1, 0, -8236284267, -287706904980021]\) | \(2559906872288885740336238809/432832410\) | \(10447522161811290\) | \([2]\) | \(238878720\) | \(3.8736\) | |
| 372810.o2 | 372810o3 | \([1, 1, 0, -517273447, -4449608527769]\) | \(634148167334363929064089/12667087050850083750\) | \(305752687718900405171403750\) | \([2]\) | \(238878720\) | \(3.8736\) | |
| 372810.o3 | 372810o2 | \([1, 1, 0, -514767817, -4495580323631]\) | \(624977448773431992007609/256987510488900\) | \(6203053766564047484100\) | \([2, 2]\) | \(119439360\) | \(3.5270\) | |
| 372810.o4 | 372810o1 | \([1, 1, 0, -32016437, -70970825379]\) | \(-150365846112551697529/3095562122018160\) | \(-74719344313999756253040\) | \([2]\) | \(59719680\) | \(3.1805\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372810.o have rank \(0\).
Complex multiplication
The elliptic curves in class 372810.o do not have complex multiplication.Modular form 372810.2.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.
