# Properties

 Label 463680.jr Number of curves $2$ Conductor $463680$ CM no Rank $2$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("jr1")

sage: E.isogeny_class()

## Elliptic curves in class 463680.jr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.jr1 463680jr1 $$[0, 0, 0, -81612, 8803216]$$ $$8493409990827/185150000$$ $$1310470963200000$$ $$$$ $$1966080$$ $$1.6890$$ $$\Gamma_0(N)$$-optimal
463680.jr2 463680jr2 $$[0, 0, 0, 6708, 26855824]$$ $$4716275733/44023437500$$ $$-311592960000000000$$ $$$$ $$3932160$$ $$2.0356$$

## Rank

sage: E.rank()

The elliptic curves in class 463680.jr have rank $$2$$.

## Complex multiplication

The elliptic curves in class 463680.jr do not have complex multiplication.

## Modular form 463680.2.a.jr

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 2q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 