Properties

 Label 12480bh Number of curves $4$ Conductor $12480$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

Elliptic curves in class 12480bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.cx3 12480bh1 $$[0, 1, 0, -260, 1530]$$ $$30488290624/195$$ $$12480$$ $$$$ $$1536$$ $$-0.029371$$ $$\Gamma_0(N)$$-optimal
12480.cx2 12480bh2 $$[0, 1, 0, -265, 1463]$$ $$504358336/38025$$ $$155750400$$ $$[2, 2]$$ $$3072$$ $$0.31720$$
12480.cx1 12480bh3 $$[0, 1, 0, -865, -8257]$$ $$2186875592/428415$$ $$14038302720$$ $$$$ $$6144$$ $$0.66378$$
12480.cx4 12480bh4 $$[0, 1, 0, 255, 6975]$$ $$55742968/658125$$ $$-21565440000$$ $$$$ $$6144$$ $$0.66378$$

Rank

sage: E.rank()

The elliptic curves in class 12480bh have rank $$0$$.

Complex multiplication

The elliptic curves in class 12480bh do not have complex multiplication.

Modular form 12480.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + q^{13} + q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})$$ 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 Cremona 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 Cremona labels. 