Properties

 Label 64680dj Number of curves $4$ Conductor $64680$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("dj1")

sage: E.isogeny_class()

Elliptic curves in class 64680dj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64680.dl4 64680dj1 $$[0, 1, 0, 17820, -871200]$$ $$20777545136/23059575$$ $$-694511600428800$$ $$$$ $$196608$$ $$1.5344$$ $$\Gamma_0(N)$$-optimal
64680.dl3 64680dj2 $$[0, 1, 0, -100760, -8270592]$$ $$939083699236/300155625$$ $$36160521344640000$$ $$[2, 2]$$ $$393216$$ $$1.8809$$
64680.dl2 64680dj3 $$[0, 1, 0, -639760, 190512608]$$ $$120186986927618/4332064275$$ $$1043789885213644800$$ $$$$ $$786432$$ $$2.2275$$
64680.dl1 64680dj4 $$[0, 1, 0, -1459040, -678717600]$$ $$1425631925916578/270703125$$ $$65224605600000000$$ $$$$ $$786432$$ $$2.2275$$

Rank

sage: E.rank()

The elliptic curves in class 64680dj have rank $$0$$.

Complex multiplication

The elliptic curves in class 64680dj do not have complex multiplication.

Modular form 64680.2.a.dj

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + q^{11} + 2 q^{13} + q^{15} + 2 q^{17} + O(q^{20})$$ 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 