Properties

Label 24384bi
Number of curves $2$
Conductor $24384$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 24384bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24384.bj2 24384bi1 \([0, 1, 0, -6524545, -6356293249]\) \(117174888570509216929/1273887851544576\) \(333942056955301330944\) \([]\) \(709632\) \(2.7532\) \(\Gamma_0(N)\)-optimal
24384.bj1 24384bi2 \([0, 1, 0, -1431110785, 20837616542591]\) \(1236526859255318155975783969/38367061931916216\) \(10057695083080244527104\) \([]\) \(4967424\) \(3.7262\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24384bi have rank \(1\).

Complex multiplication

The elliptic curves in class 24384bi do not have complex multiplication.

Modular form 24384.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + 5 q^{11} + q^{15} - 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.