Properties

 Label 361920.bb Number of curves $2$ Conductor $361920$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 361920.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361920.bb1 361920bb1 $$[0, -1, 0, -53281, 4044961]$$ $$63812982460681/10201800960$$ $$2674340910858240$$ $$$$ $$1474560$$ $$1.6826$$ $$\Gamma_0(N)$$-optimal
361920.bb2 361920bb2 $$[0, -1, 0, 95199, 22426785]$$ $$363979050334199/1041836936400$$ $$-273111301855641600$$ $$$$ $$2949120$$ $$2.0292$$

Rank

sage: E.rank()

The elliptic curves in class 361920.bb have rank $$1$$.

Complex multiplication

The elliptic curves in class 361920.bb do not have complex multiplication.

Modular form 361920.2.a.bb

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} + q^{15} - 4 q^{17} + O(q^{20})$$ 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. 