Properties

 Label 229320dp Number of curves $2$ Conductor $229320$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("dp1")

sage: E.isogeny_class()

Elliptic curves in class 229320dp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.a1 229320dp1 $$[0, 0, 0, -765723, -257800858]$$ $$565357377316/257985$$ $$22657405671613440$$ $$[2]$$ $$3538944$$ $$2.0955$$ $$\Gamma_0(N)$$-optimal
229320.a2 229320dp2 $$[0, 0, 0, -642243, -343718242]$$ $$-166792350818/194041575$$ $$-34083211674584217600$$ $$[2]$$ $$7077888$$ $$2.4421$$

Rank

sage: E.rank()

The elliptic curves in class 229320dp have rank $$1$$.

Complex multiplication

The elliptic curves in class 229320dp do not have complex multiplication.

Modular form 229320.2.a.dp

sage: E.q_eigenform(10)

$$q - q^{5} - 6q^{11} - q^{13} - 4q^{19} + O(q^{20})$$

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.