# Properties

 Label 392.d Number of curves $4$ Conductor $392$ CM no Rank $1$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 392.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392.d1 392a3 $$[0, 0, 0, -14651, -682570]$$ $$1443468546/7$$ $$1686616064$$ $$$$ $$384$$ $$0.97092$$
392.d2 392a4 $$[0, 0, 0, -2891, 47334]$$ $$11090466/2401$$ $$578509309952$$ $$$$ $$384$$ $$0.97092$$
392.d3 392a2 $$[0, 0, 0, -931, -10290]$$ $$740772/49$$ $$5903156224$$ $$[2, 2]$$ $$192$$ $$0.62435$$
392.d4 392a1 $$[0, 0, 0, 49, -686]$$ $$432/7$$ $$-210827008$$ $$$$ $$96$$ $$0.27778$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 392.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 392.d do not have complex multiplication.

## Modular form392.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{5} - 3q^{9} - 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 