# Properties

 Label 289800e Number of curves $2$ Conductor $289800$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 289800e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.e1 289800e1 $$[0, 0, 0, -2175, -10750]$$ $$10536048/5635$$ $$608580000000$$ $$$$ $$368640$$ $$0.95246$$ $$\Gamma_0(N)$$-optimal
289800.e2 289800e2 $$[0, 0, 0, 8325, -84250]$$ $$147704148/92575$$ $$-39992400000000$$ $$$$ $$737280$$ $$1.2990$$

## Rank

sage: E.rank()

The elliptic curves in class 289800e have rank $$2$$.

## Complex multiplication

The elliptic curves in class 289800e do not have complex multiplication.

## Modular form 289800.2.a.e

sage: E.q_eigenform(10)

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