Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.b1 229320z1 \([0, 0, 0, -210063, 34277362]\) \(46689225424/3901625\) \(85664573912736000\) \([2]\) \(2654208\) \(1.9910\) \(\Gamma_0(N)\)-optimal
229320.b2 229320z2 \([0, 0, 0, 222117, 157102918]\) \(13799183324/129390625\) \(-11363667968016000000\) \([2]\) \(5308416\) \(2.3376\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.b

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