# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dj1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.dj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.dj1 92400w4 $$[0, -1, 0, -407367408, 2803021257312]$$ $$233632133015204766393938/29145526885986328125$$ $$932656860351562500000000000$$ $$$$ $$47185920$$ $$3.9047$$
92400.dj2 92400w2 $$[0, -1, 0, -101754408, -349682450688]$$ $$7282213870869695463556/912102595400390625$$ $$14593641526406250000000000$$ $$[2, 2]$$ $$23592960$$ $$3.5581$$
92400.dj3 92400w1 $$[0, -1, 0, -98473908, -376083914688]$$ $$26401417552259125806544/507547744790625$$ $$2030190979162500000000$$ $$$$ $$11796480$$ $$3.2115$$ $$\Gamma_0(N)$$-optimal
92400.dj4 92400w3 $$[0, -1, 0, 151370592, -1812744950688]$$ $$11986661998777424518222/51295853620928503125$$ $$-1641467315869712100000000000$$ $$$$ $$47185920$$ $$3.9047$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.dj

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + q^{11} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 