Properties

Label 2400.a
Number of curves $4$
Conductor $2400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2400.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.a1 2400v2 \([0, -1, 0, -90033, -10368063]\) \(1261112198464/675\) \(43200000000\) \([2]\) \(9216\) \(1.3704\)  
2400.a2 2400v3 \([0, -1, 0, -12408, 300312]\) \(26410345352/10546875\) \(84375000000000\) \([2]\) \(9216\) \(1.3704\)  
2400.a3 2400v1 \([0, -1, 0, -5658, -158688]\) \(20034997696/455625\) \(455625000000\) \([2, 2]\) \(4608\) \(1.0238\) \(\Gamma_0(N)\)-optimal
2400.a4 2400v4 \([0, -1, 0, 592, -496188]\) \(2863288/13286025\) \(-106288200000000\) \([2]\) \(9216\) \(1.3704\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2400.a have rank \(0\).

Complex multiplication

The elliptic curves in class 2400.a do not have complex multiplication.

Modular form 2400.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.