Properties

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

Related objects

Show commands: SageMath
sage: E = EllipticCurve("dv1")

sage: E.isogeny_class()

Elliptic curves in class 229320dv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ba1 229320dv1 $$[0, 0, 0, -5963643, 5605479558]$$ $$267080942160036/1990625$$ $$174825661046400000$$ $$[2]$$ $$6881280$$ $$2.4845$$ $$\Gamma_0(N)$$-optimal
229320.ba2 229320dv2 $$[0, 0, 0, -5840163, 5848710462]$$ $$-125415986034978/11552734375$$ $$-2029226422860000000000$$ $$[2]$$ $$13762560$$ $$2.8311$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 229320.2.a.dv

sage: E.q_eigenform(10)

$$q - q^{5} - 2q^{11} - q^{13} - 8q^{19} + O(q^{20})$$

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 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.