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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 35280fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.fp6 | 35280fq1 | \([0, 0, 0, 70413, 10064306]\) | \(109902239/188160\) | \(-66100237628866560\) | \([2]\) | \(294912\) | \(1.9124\) | \(\Gamma_0(N)\)-optimal |
| 35280.fp5 | 35280fq2 | \([0, 0, 0, -494067, 104106674]\) | \(37966934881/8643600\) | \(3036479666076057600\) | \([2, 2]\) | \(589824\) | \(2.2590\) | |
| 35280.fp4 | 35280fq3 | \([0, 0, 0, -2610867, -1534719886]\) | \(5602762882081/345888060\) | \(121509794637476904960\) | \([2]\) | \(1179648\) | \(2.6056\) | |
| 35280.fp2 | 35280fq4 | \([0, 0, 0, -7408947, 7761644786]\) | \(128031684631201/9922500\) | \(3485754718709760000\) | \([2, 2]\) | \(1179648\) | \(2.6056\) | |
| 35280.fp3 | 35280fq5 | \([0, 0, 0, -6915027, 8841057554]\) | \(-104094944089921/35880468750\) | \(-12604738045334400000000\) | \([2]\) | \(2359296\) | \(2.9522\) | |
| 35280.fp1 | 35280fq6 | \([0, 0, 0, -118540947, 496764671186]\) | \(524388516989299201/3150\) | \(1106588799590400\) | \([2]\) | \(2359296\) | \(2.9522\) |
Rank
sage: E.rank()
The elliptic curves in class 35280fq have rank \(1\).
Complex multiplication
The elliptic curves in class 35280fq do not have complex multiplication.Modular form 35280.2.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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
