Properties

 Label 119952.bm Number of curves $2$ Conductor $119952$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

Elliptic curves in class 119952.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bm1 119952ba1 $$[0, 0, 0, -4746, 123235]$$ $$2955053056/70227$$ $$280960810704$$ $$[2]$$ $$143360$$ $$0.98187$$ $$\Gamma_0(N)$$-optimal
119952.bm2 119952ba2 $$[0, 0, 0, 609, 385630]$$ $$390224/1003833$$ $$-64257390118656$$ $$[2]$$ $$286720$$ $$1.3284$$

Rank

sage: E.rank()

The elliptic curves in class 119952.bm have rank $$1$$.

Complex multiplication

The elliptic curves in class 119952.bm do not have complex multiplication.

Modular form 119952.2.a.bm

sage: E.q_eigenform(10)

$$q - 2q^{5} - 2q^{11} + 4q^{13} - q^{17} + 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.