Properties

Label 2394.b
Number of curves $4$
Conductor $2394$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2394.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.b1 2394f4 \([1, -1, 0, -10953, 443961]\) \(199350693197713/547428\) \(399075012\) \([2]\) \(2048\) \(0.88357\)  
2394.b2 2394f3 \([1, -1, 0, -1953, -24111]\) \(1130389181713/295568028\) \(215469092412\) \([2]\) \(2048\) \(0.88357\)  
2394.b3 2394f2 \([1, -1, 0, -693, 6885]\) \(50529889873/2547216\) \(1856920464\) \([2, 2]\) \(1024\) \(0.53699\)  
2394.b4 2394f1 \([1, -1, 0, 27, 405]\) \(2924207/102144\) \(-74462976\) \([2]\) \(512\) \(0.19042\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2394.b have rank \(1\).

Complex multiplication

The elliptic curves in class 2394.b do not have complex multiplication.

Modular form 2394.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} + 2 q^{10} + 2 q^{13} + q^{14} + q^{16} + 2 q^{17} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.