Properties

Label 1470.i
Number of curves $2$
Conductor $1470$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 1470.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.i1 1470i1 \([1, 0, 1, -52358, 2625368]\) \(393349474783/153600000\) \(6198314035200000\) \([2]\) \(15680\) \(1.7290\) \(\Gamma_0(N)\)-optimal
1470.i2 1470i2 \([1, 0, 1, 167162, 18957656]\) \(12801408679457/11250000000\) \(-453978078750000000\) \([2]\) \(31360\) \(2.0755\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1470.i have rank \(0\).

Complex multiplication

The elliptic curves in class 1470.i do not have complex multiplication.

Modular form 1470.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + 6 q^{11} + q^{12} + 6 q^{13} + q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.