Properties

Label 34496.dd
Number of curves $2$
Conductor $34496$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dd1")
 
E.isogeny_class()
 

Elliptic curves in class 34496.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34496.dd1 34496u2 \([0, -1, 0, -735457, 243008865]\) \(1426487591593/2156\) \(66493151707136\) \([2]\) \(294912\) \(1.9204\)  
34496.dd2 34496u1 \([0, -1, 0, -45537, 3882593]\) \(-338608873/13552\) \(-417956953587712\) \([2]\) \(147456\) \(1.5738\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34496.dd have rank \(0\).

Complex multiplication

The elliptic curves in class 34496.dd do not have complex multiplication.

Modular form 34496.2.a.dd

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