# Properties

 Label 8379.j Number of curves $3$ Conductor $8379$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 8379.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8379.j1 8379f3 $$[0, 0, 1, -339276, -76063766]$$ $$-50357871050752/19$$ $$-1629556299$$ $$[]$$ $$27216$$ $$1.5557$$
8379.j2 8379f2 $$[0, 0, 1, -4116, -108131]$$ $$-89915392/6859$$ $$-588269823939$$ $$[]$$ $$9072$$ $$1.0064$$
8379.j3 8379f1 $$[0, 0, 1, 294, -86]$$ $$32768/19$$ $$-1629556299$$ $$[]$$ $$3024$$ $$0.45709$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8379.j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8379.j do not have complex multiplication.

## Modular form8379.2.a.j

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} - 3q^{11} + 4q^{13} + 4q^{16} - 3q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 