Properties

Label 290400.ca
Number of curves $4$
Conductor $290400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 290400.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
290400.ca1 290400ca4 \([0, -1, 0, -246033, -46848063]\) \(14526784/15\) \(1700698560000000\) \([2]\) \(1966080\) \(1.8404\)  
290400.ca2 290400ca2 \([0, -1, 0, -170408, 26886312]\) \(38614472/405\) \(5739857640000000\) \([2]\) \(1966080\) \(1.8404\)  
290400.ca3 290400ca1 \([0, -1, 0, -19158, -338688]\) \(438976/225\) \(398601225000000\) \([2, 2]\) \(983040\) \(1.4938\) \(\Gamma_0(N)\)-optimal
290400.ca4 290400ca3 \([0, -1, 0, 71592, -2698188]\) \(2863288/1875\) \(-26573415000000000\) \([2]\) \(1966080\) \(1.8404\)  

Rank

sage: E.rank()
 

The elliptic curves in class 290400.ca have rank \(0\).

Complex multiplication

The elliptic curves in class 290400.ca do not have complex multiplication.

Modular form 290400.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 2 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.