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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 25200.fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.fq1 | 25200er6 | \([0, 0, 0, -60480075, -181036687750]\) | \(524388516989299201/3150\) | \(146966400000000\) | \([2]\) | \(1179648\) | \(2.7839\) | |
| 25200.fq2 | 25200er4 | \([0, 0, 0, -3780075, -2828587750]\) | \(128031684631201/9922500\) | \(462944160000000000\) | \([2, 2]\) | \(589824\) | \(2.4374\) | |
| 25200.fq3 | 25200er5 | \([0, 0, 0, -3528075, -3221959750]\) | \(-104094944089921/35880468750\) | \(-1674039150000000000000\) | \([2]\) | \(1179648\) | \(2.7839\) | |
| 25200.fq4 | 25200er3 | \([0, 0, 0, -1332075, 559300250]\) | \(5602762882081/345888060\) | \(16137753327360000000\) | \([4]\) | \(589824\) | \(2.4374\) | |
| 25200.fq5 | 25200er2 | \([0, 0, 0, -252075, -37939750]\) | \(37966934881/8643600\) | \(403275801600000000\) | \([2, 2]\) | \(294912\) | \(2.0908\) | |
| 25200.fq6 | 25200er1 | \([0, 0, 0, 35925, -3667750]\) | \(109902239/188160\) | \(-8778792960000000\) | \([2]\) | \(147456\) | \(1.7442\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 25200.fq do not have complex multiplication.Modular form 25200.2.a.fq
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.
