Properties

 Label 93600.be Number of curves $2$ Conductor $93600$ CM no Rank $2$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

Elliptic curves in class 93600.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.be1 93600ba2 $$[0, 0, 0, -295500, 61792000]$$ $$61162984000/41067$$ $$1916021952000000$$ $$[2]$$ $$737280$$ $$1.8708$$
93600.be2 93600ba1 $$[0, 0, 0, -22125, 556000]$$ $$1643032000/767637$$ $$559607373000000$$ $$[2]$$ $$368640$$ $$1.5243$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 93600.be have rank $$2$$.

Complex multiplication

The elliptic curves in class 93600.be do not have complex multiplication.

Modular form 93600.2.a.be

sage: E.q_eigenform(10)

$$q - 2q^{7} - 4q^{11} - q^{13} - 6q^{17} + 6q^{19} + O(q^{20})$$

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.