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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 34914.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34914.o1 | 34914o3 | \([1, 0, 1, -42596, 3367202]\) | \(57736239625/255552\) | \(37830867505728\) | \([2]\) | \(142560\) | \(1.4577\) | |
| 34914.o2 | 34914o4 | \([1, 0, 1, -21436, 6718946]\) | \(-7357983625/127552392\) | \(-18882331743796488\) | \([2]\) | \(285120\) | \(1.8042\) | |
| 34914.o3 | 34914o1 | \([1, 0, 1, -2921, -57544]\) | \(18609625/1188\) | \(175866636132\) | \([2]\) | \(47520\) | \(0.90836\) | \(\Gamma_0(N)\)-optimal |
| 34914.o4 | 34914o2 | \([1, 0, 1, 2369, -241636]\) | \(9938375/176418\) | \(-26116195465602\) | \([2]\) | \(95040\) | \(1.2549\) |
Rank
sage: E.rank()
The elliptic curves in class 34914.o have rank \(0\).
Complex multiplication
The elliptic curves in class 34914.o do not have complex multiplication.Modular form 34914.2.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.
