Properties

Label 14994s
Number of curves $2$
Conductor $14994$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 14994s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.v2 14994s1 \([1, -1, 0, -7947, -269487]\) \(647214625/3332\) \(285772715172\) \([2]\) \(18432\) \(1.0441\) \(\Gamma_0(N)\)-optimal
14994.v1 14994s2 \([1, -1, 0, -12357, 66555]\) \(2433138625/1387778\) \(119024335869138\) \([2]\) \(36864\) \(1.3907\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14994s have rank \(1\).

Complex multiplication

The elliptic curves in class 14994s do not have complex multiplication.

Modular form 14994.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} + 2 q^{11} + 2 q^{13} + q^{16} - q^{17} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.