Properties

 Label 1950bb Number of curves $2$ Conductor $1950$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

Elliptic curves in class 1950bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.v2 1950bb1 $$[1, 0, 0, -323, -63]$$ $$29819839301/17252352$$ $$2156544000$$ $$[2]$$ $$1792$$ $$0.48045$$ $$\Gamma_0(N)$$-optimal
1950.v1 1950bb2 $$[1, 0, 0, -3523, 79937]$$ $$38686490446661/141927552$$ $$17740944000$$ $$[2]$$ $$3584$$ $$0.82703$$

Rank

sage: E.rank()

The elliptic curves in class 1950bb have rank $$1$$.

Complex multiplication

The elliptic curves in class 1950bb do not have complex multiplication.

Modular form1950.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} - 6q^{11} + q^{12} + q^{13} - 4q^{14} + q^{16} - 4q^{17} + q^{18} + 2q^{19} + O(q^{20})$$

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 Cremona 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 Cremona labels.