Properties

 Label 4560.l Number of curves $4$ Conductor $4560$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

Elliptic curves in class 4560.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.l1 4560c3 $$[0, -1, 0, -32840, 2301600]$$ $$3825131988299044/961875$$ $$984960000$$ $$$$ $$10240$$ $$1.1008$$
4560.l2 4560c2 $$[0, -1, 0, -2060, 36192]$$ $$3778298043856/59213025$$ $$15158534400$$ $$[2, 2]$$ $$5120$$ $$0.75427$$
4560.l3 4560c1 $$[0, -1, 0, -255, -630]$$ $$115060504576/52780005$$ $$844480080$$ $$$$ $$2560$$ $$0.40769$$ $$\Gamma_0(N)$$-optimal
4560.l4 4560c4 $$[0, -1, 0, -160, 98512]$$ $$-445138564/4089438495$$ $$-4187585018880$$ $$$$ $$10240$$ $$1.1008$$

Rank

sage: E.rank()

The elliptic curves in class 4560.l have rank $$0$$.

Complex multiplication

The elliptic curves in class 4560.l do not have complex multiplication.

Modular form4560.2.a.l

sage: E.q_eigenform(10)

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