# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("fy1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.fy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.fy1 92400gi2 $$[0, 1, 0, -36229908, 83913539688]$$ $$1314817350433665559504/190690249278375$$ $$762760997113500000000$$ $$$$ $$7741440$$ $$3.0219$$
92400.fy2 92400gi1 $$[0, 1, 0, -2058033, 1559320938]$$ $$-3856034557002072064/1973796785296875$$ $$-493449196324218750000$$ $$$$ $$3870720$$ $$2.6753$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 92400.fy have rank $$0$$.

## Complex multiplication

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

## Modular form 92400.2.a.fy

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} + q^{11} + 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 