Properties

Label 229320bd
Number of curves $2$
Conductor $229320$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 229320bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.p2 229320bd1 \([0, 0, 0, -24313774863, 1440890341256338]\) \(211072197308055014773168/3052652281946850375\) \(22989376442788411365653213088000\) \([2]\) \(586629120\) \(4.8216\) \(\Gamma_0(N)\)-optimal
229320.p1 229320bd2 \([0, 0, 0, -47237404683, -1708949353064618]\) \(386965237776463086681532/182055746334444328125\) \(5484212022190882548541676976000000\) \([2]\) \(1173258240\) \(5.1682\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320bd have rank \(1\).

Complex multiplication

The elliptic curves in class 229320bd do not have complex multiplication.

Modular form 229320.2.a.bd

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.