Properties

Label 14896.a
Number of curves $3$
Conductor $14896$
CM no
Rank $0$
Graph

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

Elliptic curves in class 14896.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14896.a1 14896bg3 \([0, 1, 0, -603157, -180500349]\) \(-50357871050752/19\) \(-9155915776\) \([]\) \(81648\) \(1.6995\)  
14896.a2 14896bg2 \([0, 1, 0, -7317, -258749]\) \(-89915392/6859\) \(-3305285595136\) \([]\) \(27216\) \(1.1502\)  
14896.a3 14896bg1 \([0, 1, 0, 523, -29]\) \(32768/19\) \(-9155915776\) \([]\) \(9072\) \(0.60093\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14896.a have rank \(0\).

Complex multiplication

The elliptic curves in class 14896.a do not have complex multiplication.

Modular form 14896.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - 3q^{5} + q^{9} - 3q^{11} + 4q^{13} + 6q^{15} + 3q^{17} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.