Properties

 Label 327990.bi Number of curves $2$ Conductor $327990$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

Elliptic curves in class 327990.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bi1 327990bi1 $$[1, 0, 0, -419256, 104243760]$$ $$13701674594089/31758480$$ $$18890684543512080$$ $$$$ $$4730880$$ $$2.0038$$ $$\Gamma_0(N)$$-optimal
327990.bi2 327990bi2 $$[1, 0, 0, -267876, 180569556]$$ $$-3573857582569/21617820900$$ $$-12858784020521208900$$ $$$$ $$9461760$$ $$2.3504$$

Rank

sage: E.rank()

The elliptic curves in class 327990.bi have rank $$0$$.

Complex multiplication

The elliptic curves in class 327990.bi do not have complex multiplication.

Modular form 327990.2.a.bi

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} + 2 q^{11} + q^{12} + q^{13} - 2 q^{14} - q^{15} + q^{16} + 6 q^{17} + q^{18} + 2 q^{19} + O(q^{20})$$ 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. 