Properties

 Label 2880.j Number of curves $4$ Conductor $2880$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 2880.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.j1 2880y3 $$[0, 0, 0, -2028, 34832]$$ $$38614472/405$$ $$9674588160$$ $$[2]$$ $$2048$$ $$0.73261$$
2880.j2 2880y2 $$[0, 0, 0, -228, -448]$$ $$438976/225$$ $$671846400$$ $$[2, 2]$$ $$1024$$ $$0.38604$$
2880.j3 2880y1 $$[0, 0, 0, -183, -952]$$ $$14526784/15$$ $$699840$$ $$[2]$$ $$512$$ $$0.039465$$ $$\Gamma_0(N)$$-optimal
2880.j4 2880y4 $$[0, 0, 0, 852, -3472]$$ $$2863288/1875$$ $$-44789760000$$ $$[2]$$ $$2048$$ $$0.73261$$

Rank

sage: E.rank()

The elliptic curves in class 2880.j have rank $$1$$.

Complex multiplication

The elliptic curves in class 2880.j do not have complex multiplication.

Modular form2880.2.a.j

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{11} - 2q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$

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 LMFDB 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 LMFDB labels.