Properties

Label 297024.b
Number of curves $2$
Conductor $297024$
CM no
Rank $2$
Graph

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

Elliptic curves in class 297024.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297024.b1 297024b1 \([0, -1, 0, -645, -1899]\) \(29025255424/14911533\) \(15269409792\) \([2]\) \(368640\) \(0.64628\) \(\Gamma_0(N)\)-optimal
297024.b2 297024b2 \([0, -1, 0, 2415, -17199]\) \(95033195696/62082657\) \(-1017162252288\) \([2]\) \(737280\) \(0.99286\)  

Rank

sage: E.rank()
 

The elliptic curves in class 297024.b have rank \(2\).

Complex multiplication

The elliptic curves in class 297024.b do not have complex multiplication.

Modular form 297024.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} - q^{7} + q^{9} - q^{13} + 4 q^{15} - q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.