Properties

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

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

Elliptic curves in class 2394b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.c2 2394b1 \([1, -1, 0, -139692, 20130768]\) \(11165451838341046875/572244736\) \(15450607872\) \([6]\) \(9216\) \(1.4280\) \(\Gamma_0(N)\)-optimal
2394.c3 2394b2 \([1, -1, 0, -139452, 20203200]\) \(-11108001800138902875/79947274872976\) \(-2158576421570352\) \([6]\) \(18432\) \(1.7746\)  
2394.c1 2394b3 \([1, -1, 0, -152187, 16325477]\) \(19804628171203875/5638671302656\) \(110985967250178048\) \([2]\) \(27648\) \(1.9774\)  
2394.c4 2394b4 \([1, -1, 0, 400773, 107342693]\) \(361682234074684125/462672528510976\) \(-9106783378681540608\) \([2]\) \(55296\) \(2.3239\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2394.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 6 q^{11} + 2 q^{13} - q^{14} + q^{16} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.