Properties

 Label 3360d Number of curves $4$ Conductor $3360$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 3360d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.a3 3360d1 $$[0, -1, 0, -26, -24]$$ $$31554496/11025$$ $$705600$$ $$[2, 2]$$ $$512$$ $$-0.17631$$ $$\Gamma_0(N)$$-optimal
3360.a1 3360d2 $$[0, -1, 0, -376, -2684]$$ $$11512557512/2835$$ $$1451520$$ $$[2]$$ $$1024$$ $$0.17027$$
3360.a2 3360d3 $$[0, -1, 0, -176, 936]$$ $$1184287112/36015$$ $$18439680$$ $$[2]$$ $$1024$$ $$0.17027$$
3360.a4 3360d4 $$[0, -1, 0, 79, -255]$$ $$13144256/13125$$ $$-53760000$$ $$[2]$$ $$1024$$ $$0.17027$$

Rank

sage: E.rank()

The elliptic curves in class 3360d have rank $$1$$.

Complex multiplication

The elliptic curves in class 3360d do not have complex multiplication.

Modular form3360.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 6q^{13} + q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.