Properties

Label 390.f
Number of curves $6$
Conductor $390$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390.f1 390b5 \([1, 1, 1, -9015, -333213]\) \(81025909800741361/11088090\) \(11088090\) \([2]\) \(512\) \(0.76407\)  
390.f2 390b4 \([1, 1, 1, -845, 9095]\) \(66730743078481/60937500\) \(60937500\) \([4]\) \(256\) \(0.41750\)  
390.f3 390b3 \([1, 1, 1, -565, -5353]\) \(19948814692561/231344100\) \(231344100\) \([2, 2]\) \(256\) \(0.41750\)  
390.f4 390b6 \([1, 1, 1, -115, -13093]\) \(-168288035761/73415764890\) \(-73415764890\) \([2]\) \(512\) \(0.76407\)  
390.f5 390b2 \([1, 1, 1, -65, 47]\) \(30400540561/15210000\) \(15210000\) \([2, 4]\) \(128\) \(0.070926\)  
390.f6 390b1 \([1, 1, 1, 15, 15]\) \(371694959/249600\) \(-249600\) \([4]\) \(64\) \(-0.27565\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 390.f have rank \(0\).

Complex multiplication

The elliptic curves in class 390.f do not have complex multiplication.

Modular form 390.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + q^{13} - q^{15} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.