Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7350.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7350.p1 | 7350g5 | \([1, 1, 0, -20580025, 35926369375]\) | \(524388516989299201/3150\) | \(5790536718750\) | \([2]\) | \(294912\) | \(2.5144\) | |
| 7350.p2 | 7350g4 | \([1, 1, 0, -1286275, 560925625]\) | \(128031684631201/9922500\) | \(18240190664062500\) | \([2, 2]\) | \(147456\) | \(2.1679\) | |
| 7350.p3 | 7350g6 | \([1, 1, 0, -1200525, 639043875]\) | \(-104094944089921/35880468750\) | \(-65957832312011718750\) | \([2]\) | \(294912\) | \(2.5144\) | |
| 7350.p4 | 7350g3 | \([1, 1, 0, -453275, -111207375]\) | \(5602762882081/345888060\) | \(635834130795937500\) | \([2]\) | \(147456\) | \(2.1679\) | |
| 7350.p5 | 7350g2 | \([1, 1, 0, -85775, 7495125]\) | \(37966934881/8643600\) | \(15889232756250000\) | \([2, 2]\) | \(73728\) | \(1.8213\) | |
| 7350.p6 | 7350g1 | \([1, 1, 0, 12225, 733125]\) | \(109902239/188160\) | \(-345888060000000\) | \([2]\) | \(36864\) | \(1.4747\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.p have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.p do not have complex multiplication.Modular form 7350.2.a.p
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
