Properties

Label 30960.f
Number of curves $4$
Conductor $30960$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 30960.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.f1 30960bf4 \([0, 0, 0, -746283, -214116262]\) \(15393836938735081/2275690697640\) \(6795176012101877760\) \([2]\) \(552960\) \(2.3382\)  
30960.f2 30960bf3 \([0, 0, 0, -717483, -233913382]\) \(13679527032530281/381633600\) \(1139551823462400\) \([2]\) \(276480\) \(1.9917\)  
30960.f3 30960bf2 \([0, 0, 0, -195483, 33231818]\) \(276670733768281/336980250\) \(1006217634816000\) \([2]\) \(184320\) \(1.7889\)  
30960.f4 30960bf1 \([0, 0, 0, -15483, 219818]\) \(137467988281/72562500\) \(216670464000000\) \([2]\) \(92160\) \(1.4423\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.f have rank \(1\).

Complex multiplication

The elliptic curves in class 30960.f do not have complex multiplication.

Modular form 30960.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2q^{7} - 6q^{11} + 2q^{13} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.