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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 227430.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227430.dg1 | 227430bq6 | \([1, -1, 1, -1155068303, -15106590706863]\) | \(4969327007303723277361/1123462695162150\) | \(38530779060848044976425350\) | \([2]\) | \(176947200\) | \(3.9017\) | |
| 227430.dg2 | 227430bq4 | \([1, -1, 1, -80461553, -178583578563]\) | \(1679731262160129361/570261564022500\) | \(19557945648629907499102500\) | \([2, 2]\) | \(88473600\) | \(3.5551\) | |
| 227430.dg3 | 227430bq2 | \([1, -1, 1, -33091133, 71210120181]\) | \(116844823575501841/3760263939600\) | \(128963693846808322160400\) | \([2, 2]\) | \(44236800\) | \(3.2086\) | |
| 227430.dg4 | 227430bq1 | \([1, -1, 1, -32831213, 72414797397]\) | \(114113060120923921/124104960\) | \(4256359213979255040\) | \([2]\) | \(22118400\) | \(2.8620\) | \(\Gamma_0(N)\)-optimal |
| 227430.dg5 | 227430bq3 | \([1, -1, 1, 10120567, 243901358061]\) | \(3342636501165359/751262567039460\) | \(-25765637000617165991445540\) | \([2]\) | \(88473600\) | \(3.5551\) | |
| 227430.dg6 | 227430bq5 | \([1, -1, 1, 236218477, -1237941614919]\) | \(42502666283088696719/43898058864843750\) | \(-1505547460191610492502343750\) | \([2]\) | \(176947200\) | \(3.9017\) |
Rank
sage: E.rank()
The elliptic curves in class 227430.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 227430.dg do not have complex multiplication.Modular form 227430.2.a.dg
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
