# Properties

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

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)

$$q - q^{3} - q^{7} + q^{9} + q^{11} - q^{13} - 6q^{17} - 5q^{19} + O(q^{20})$$ ## 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. 