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Properties

Label 155526dd
Number of curves $2$
Conductor $155526$
CM no
Rank $1$
Graph

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

Elliptic curves in class 155526dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.m2 155526dd1 \([1, 1, 0, 608604, -223881552]\) \(596183/864\) \(-36129434059766615904\) \([]\) \(5322240\) \(2.4383\) \(\Gamma_0(N)\)-optimal
155526.m1 155526dd2 \([1, 1, 0, -18443331, -30649821747]\) \(-16591834777/98304\) \(-4110726719689001631744\) \([]\) \(15966720\) \(2.9876\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155526dd have rank \(1\).

Complex multiplication

The elliptic curves in class 155526dd do not have complex multiplication.

Modular form 155526.2.a.dd

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} + q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 4 q^{13} - 3 q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.