Properties

Label 32340.q
Number of curves $4$
Conductor $32340$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.q1 32340p4 \([0, -1, 0, -76260, 4428600]\) \(1628514404944/664335375\) \(20008548488544000\) \([2]\) \(248832\) \(1.8256\)  
32340.q2 32340p2 \([0, -1, 0, -35100, -2519208]\) \(158792223184/16335\) \(491979882240\) \([2]\) \(82944\) \(1.2763\)  
32340.q3 32340p1 \([0, -1, 0, -2025, -45198]\) \(-488095744/200475\) \(-377370932400\) \([2]\) \(41472\) \(0.92968\) \(\Gamma_0(N)\)-optimal
32340.q4 32340p3 \([0, -1, 0, 15615, 496350]\) \(223673040896/187171875\) \(-352329342750000\) \([2]\) \(124416\) \(1.4790\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32340.q have rank \(0\).

Complex multiplication

The elliptic curves in class 32340.q do not have complex multiplication.

Modular form 32340.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.