Properties

Label 3136.d
Number of curves $2$
Conductor $3136$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 3136.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.d1 3136m2 \([0, 1, 0, -289, 1791]\) \(238328\) \(11239424\) \([2]\) \(1024\) \(0.20753\)  
3136.d2 3136m1 \([0, 1, 0, -9, 55]\) \(-64\) \(-1404928\) \([2]\) \(512\) \(-0.13904\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3136.d have rank \(2\).

Complex multiplication

The elliptic curves in class 3136.d do not have complex multiplication.

Modular form 3136.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.