Properties

Label 240448cb
Number of curves $2$
Conductor $240448$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 240448cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
240448.cb1 240448cb1 \([0, -1, 0, -1100897, 444918497]\) \(23320116793/2873\) \(18178961765040128\) \([2]\) \(3538944\) \(2.1433\) \(\Gamma_0(N)\)-optimal
240448.cb2 240448cb2 \([0, -1, 0, -1008417, 522657185]\) \(-17923019113/8254129\) \(-52228157150960287744\) \([2]\) \(7077888\) \(2.4899\)  

Rank

sage: E.rank()
 

The elliptic curves in class 240448cb have rank \(2\).

Complex multiplication

The elliptic curves in class 240448cb do not have complex multiplication.

Modular form 240448.2.a.cb

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + 2 q^{5} - 2 q^{7} + q^{9} - 6 q^{11} + q^{13} + 4 q^{15} - 4 q^{19} + O(q^{20})\) 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.