Properties

 Label 12480.bj Number of curves $4$ Conductor $12480$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

Elliptic curves in class 12480.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.bj1 12480o3 $$[0, -1, 0, -865, 8257]$$ $$2186875592/428415$$ $$14038302720$$ $$$$ $$6144$$ $$0.66378$$
12480.bj2 12480o2 $$[0, -1, 0, -265, -1463]$$ $$504358336/38025$$ $$155750400$$ $$[2, 2]$$ $$3072$$ $$0.31720$$
12480.bj3 12480o1 $$[0, -1, 0, -260, -1530]$$ $$30488290624/195$$ $$12480$$ $$$$ $$1536$$ $$-0.029371$$ $$\Gamma_0(N)$$-optimal
12480.bj4 12480o4 $$[0, -1, 0, 255, -6975]$$ $$55742968/658125$$ $$-21565440000$$ $$$$ $$6144$$ $$0.66378$$

Rank

sage: E.rank()

The elliptic curves in class 12480.bj have rank $$1$$.

Complex multiplication

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

Modular form 12480.2.a.bj

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 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. 