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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 185130.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.dv1 | 185130bg8 | \([1, -1, 1, -123568853, -528669351669]\) | \(161572377633716256481/914742821250\) | \(1181361053517067541250\) | \([2]\) | \(20971520\) | \(3.2350\) | |
| 185130.dv2 | 185130bg3 | \([1, -1, 1, -23696663, 44405507391]\) | \(1139466686381936641/4080\) | \(5269189313520\) | \([2]\) | \(5242880\) | \(2.5418\) | |
| 185130.dv3 | 185130bg6 | \([1, -1, 1, -7862603, -7944944169]\) | \(41623544884956481/2962701562500\) | \(3826234169675001562500\) | \([2, 2]\) | \(10485760\) | \(2.8884\) | |
| 185130.dv4 | 185130bg4 | \([1, -1, 1, -1568183, 607913727]\) | \(330240275458561/67652010000\) | \(87370403953467690000\) | \([2, 2]\) | \(5242880\) | \(2.5418\) | |
| 185130.dv5 | 185130bg2 | \([1, -1, 1, -1481063, 694092831]\) | \(278202094583041/16646400\) | \(21498292399161600\) | \([2, 2]\) | \(2621440\) | \(2.1953\) | |
| 185130.dv6 | 185130bg1 | \([1, -1, 1, -87143, 12187167]\) | \(-56667352321/16711680\) | \(-21582599428177920\) | \([2]\) | \(1310720\) | \(1.8487\) | \(\Gamma_0(N)\)-optimal |
| 185130.dv7 | 185130bg5 | \([1, -1, 1, 3332317, 3644263527]\) | \(3168685387909439/6278181696900\) | \(-8108070565108416596100\) | \([2]\) | \(10485760\) | \(2.8884\) | |
| 185130.dv8 | 185130bg7 | \([1, -1, 1, 7132927, -34678975053]\) | \(31077313442863199/420227050781250\) | \(-542709775791320800781250\) | \([2]\) | \(20971520\) | \(3.2350\) |
Rank
sage: E.rank()
The elliptic curves in class 185130.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 185130.dv do not have complex multiplication.Modular form 185130.2.a.dv
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
