Properties

 Label 35904.ba Number of curves $2$ Conductor $35904$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

Elliptic curves in class 35904.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35904.ba1 35904q1 $$[0, -1, 0, -57857, 5333505]$$ $$81706955619457/744505344$$ $$195167608897536$$ $$[2]$$ $$215040$$ $$1.5643$$ $$\Gamma_0(N)$$-optimal
35904.ba2 35904q2 $$[0, -1, 0, -16897, 12698113]$$ $$-2035346265217/264305213568$$ $$-69286025905569792$$ $$[2]$$ $$430080$$ $$1.9109$$

Rank

sage: E.rank()

The elliptic curves in class 35904.ba have rank $$0$$.

Complex multiplication

The elliptic curves in class 35904.ba do not have complex multiplication.

Modular form 35904.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - 4q^{7} + q^{9} + q^{11} + 4q^{13} - 2q^{15} - q^{17} + 8q^{19} + O(q^{20})$$

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.