Properties

Label 92400.bc
Number of curves $2$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.bc1 92400fb1 \([0, -1, 0, -857701208, -9696242819088]\) \(-43612581618346739773945/147358175518034712\) \(-235773080828855539200000000\) \([]\) \(37324800\) \(3.9246\) \(\Gamma_0(N)\)-optimal
92400.bc2 92400fb2 \([0, -1, 0, 1832308792, -50399637059088]\) \(425206334414152986757655/931885180314516223488\) \(-1491016288503225957580800000000\) \([]\) \(111974400\) \(4.4739\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 92400.bc do not have complex multiplication.

Modular form 92400.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + q^{11} - q^{13} - 6q^{17} - 5q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.