# Properties

 Label 92400b Number of curves $4$ Conductor $92400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 92400b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.o4 92400b1 $$[0, -1, 0, 9092, -322688]$$ $$20777545136/23059575$$ $$-92238300000000$$ $$$$ $$196608$$ $$1.3661$$ $$\Gamma_0(N)$$-optimal
92400.o3 92400b2 $$[0, -1, 0, -51408, -2984688]$$ $$939083699236/300155625$$ $$4802490000000000$$ $$[2, 2]$$ $$393216$$ $$1.7127$$
92400.o2 92400b3 $$[0, -1, 0, -326408, 69615312]$$ $$120186986927618/4332064275$$ $$138626056800000000$$ $$$$ $$786432$$ $$2.0593$$
92400.o1 92400b4 $$[0, -1, 0, -744408, -246920688]$$ $$1425631925916578/270703125$$ $$8662500000000000$$ $$$$ $$786432$$ $$2.0593$$

## Rank

sage: E.rank()

The elliptic curves in class 92400b have rank $$1$$.

## Complex multiplication

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

## Modular form 92400.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 