Properties

 Label 2304.l Number of curves $4$ Conductor $2304$ CM no Rank $1$ Graph

Related objects

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

E.isogeny_class()

Elliptic curves in class 2304.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2304.l1 2304n4 $$[0, 0, 0, -23304, -1369280]$$ $$58591911104/243$$ $$5804752896$$ $$[2]$$ $$2560$$ $$1.0829$$
2304.l2 2304n3 $$[0, 0, 0, -1434, -22088]$$ $$-873722816/59049$$ $$-22039921152$$ $$[2]$$ $$1280$$ $$0.73631$$
2304.l3 2304n2 $$[0, 0, 0, -264, 1600]$$ $$85184/3$$ $$71663616$$ $$[2]$$ $$512$$ $$0.27816$$
2304.l4 2304n1 $$[0, 0, 0, 6, 88]$$ $$64/9$$ $$-3359232$$ $$[2]$$ $$256$$ $$-0.068409$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2304.l have rank $$1$$.

Complex multiplication

The elliptic curves in class 2304.l do not have complex multiplication.

Modular form2304.2.a.l

sage: E.q_eigenform(10)

$$q + 2 q^{5} - 2 q^{7} - 4 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.