Properties

 Label 18720.bi Number of curves $4$ Conductor $18720$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

Elliptic curves in class 18720.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18720.bi1 18720n3 $$[0, 0, 0, -9372, 349216]$$ $$30488290624/195$$ $$582266880$$ $$$$ $$12288$$ $$0.86651$$
18720.bi2 18720n2 $$[0, 0, 0, -1947, -26894]$$ $$2186875592/428415$$ $$159905041920$$ $$$$ $$12288$$ $$0.86651$$
18720.bi3 18720n1 $$[0, 0, 0, -597, 5236]$$ $$504358336/38025$$ $$1774094400$$ $$[2, 2]$$ $$6144$$ $$0.51993$$ $$\Gamma_0(N)$$-optimal
18720.bi4 18720n4 $$[0, 0, 0, 573, 23254]$$ $$55742968/658125$$ $$-245643840000$$ $$$$ $$12288$$ $$0.86651$$

Rank

sage: E.rank()

The elliptic curves in class 18720.bi have rank $$1$$.

Complex multiplication

The elliptic curves in class 18720.bi do not have complex multiplication.

Modular form 18720.2.a.bi

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 