Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 335730.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 335730.v1 | 335730v5 | \([1, 1, 0, -111014727, 450167758089]\) | \(3216206300355197383681/57660\) | \(2712665498460\) | \([2]\) | \(28311552\) | \(2.8540\) | |
| 335730.v2 | 335730v3 | \([1, 1, 0, -6938427, 7031687949]\) | \(785209010066844481/3324675600\) | \(156412292641203600\) | \([2, 2]\) | \(14155776\) | \(2.5075\) | |
| 335730.v3 | 335730v6 | \([1, 1, 0, -6830127, 7261955409]\) | \(-749011598724977281/51173462246460\) | \(-2407500615204949831260\) | \([2]\) | \(28311552\) | \(2.8540\) | |
| 335730.v4 | 335730v4 | \([1, 1, 0, -1335707, -463815699]\) | \(5601911201812801/1271193750000\) | \(59804429890443750000\) | \([2]\) | \(14155776\) | \(2.5075\) | |
| 335730.v5 | 335730v2 | \([1, 1, 0, -440427, 106119549]\) | \(200828550012481/12454560000\) | \(585935747667360000\) | \([2, 2]\) | \(7077888\) | \(2.1609\) | |
| 335730.v6 | 335730v1 | \([1, 1, 0, 21653, 6957181]\) | \(23862997439/457113600\) | \(-21505312029081600\) | \([2]\) | \(3538944\) | \(1.8143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 335730.v have rank \(2\).
Complex multiplication
The elliptic curves in class 335730.v do not have complex multiplication.Modular form 335730.2.a.v
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.
