Properties

Label 10320.m
Number of curves $4$
Conductor $10320$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 10320.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10320.m1 10320e3 \([0, -1, 0, -7960, 11392]\) \(54477543627364/31494140625\) \(32250000000000\) \([4]\) \(18432\) \(1.2815\)  
10320.m2 10320e2 \([0, -1, 0, -5380, -149600]\) \(67283921459536/260015625\) \(66564000000\) \([2, 2]\) \(9216\) \(0.93496\)  
10320.m3 10320e1 \([0, -1, 0, -5375, -149898]\) \(1073544204384256/16125\) \(258000\) \([2]\) \(4608\) \(0.58839\) \(\Gamma_0(N)\)-optimal
10320.m4 10320e4 \([0, -1, 0, -2880, -291600]\) \(-2580786074884/34615360125\) \(-35446128768000\) \([2]\) \(18432\) \(1.2815\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10320.m have rank \(0\).

Complex multiplication

The elliptic curves in class 10320.m do not have complex multiplication.

Modular form 10320.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.