Properties

Label 229320.q
Number of curves $4$
Conductor $229320$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.q1 229320be3 \([0, 0, 0, -379849323, 2849127423478]\) \(69014771940559650916/9797607421875\) \(860470050462750000000000\) \([2]\) \(70778880\) \(3.6087\)  
229320.q2 229320be4 \([0, 0, 0, -154886403, -713666478098]\) \(4678944235881273796/202428825314625\) \(17778211968841718599296000\) \([2]\) \(70778880\) \(3.6087\)  
229320.q3 229320be2 \([0, 0, 0, -25893903, 35960536402]\) \(87450143958975184/25164018140625\) \(552504377521929924000000\) \([2, 2]\) \(35389440\) \(3.2621\)  
229320.q4 229320be1 \([0, 0, 0, 4290342, 3717725893]\) \(6364491337435136/8034291412875\) \(-11025120151454371326000\) \([2]\) \(17694720\) \(2.9156\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{11} + q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.