Properties

Label 35322.d
Number of curves $2$
Conductor $35322$
CM no
Rank $0$
Graph

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

Elliptic curves in class 35322.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35322.d1 35322h2 \([1, 1, 0, -534609420, 4192138756062]\) \(1164800512406592125/150691848242418\) \(2186108639826256329090211242\) \([2]\) \(24009216\) \(3.9746\)  
35322.d2 35322h1 \([1, 1, 0, 50970470, 342887907136]\) \(1009479798755875/4084868810988\) \(-59259788133277350970048572\) \([2]\) \(12004608\) \(3.6280\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35322.d have rank \(0\).

Complex multiplication

The elliptic curves in class 35322.d do not have complex multiplication.

Modular form 35322.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - 4 q^{11} - q^{12} + 2 q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.