Properties

 Label 115920.fb Number of curves $4$ Conductor $115920$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("fb1")

sage: E.isogeny_class()

Elliptic curves in class 115920.fb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.fb1 115920ew4 $$[0, 0, 0, -727347, 238755634]$$ $$14251520160844849/264449745$$ $$789642707374080$$ $$$$ $$983040$$ $$1.9835$$
115920.fb2 115920ew2 $$[0, 0, 0, -46947, 3473314]$$ $$3832302404449/472410225$$ $$1410609373286400$$ $$[2, 2]$$ $$491520$$ $$1.6369$$
115920.fb3 115920ew1 $$[0, 0, 0, -11667, -428654]$$ $$58818484369/7455105$$ $$22260824248320$$ $$$$ $$245760$$ $$1.2903$$ $$\Gamma_0(N)$$-optimal
115920.fb4 115920ew3 $$[0, 0, 0, 68973, 17916946]$$ $$12152722588271/53476250625$$ $$-159679228746240000$$ $$$$ $$983040$$ $$1.9835$$

Rank

sage: E.rank()

The elliptic curves in class 115920.fb have rank $$1$$.

Complex multiplication

The elliptic curves in class 115920.fb do not have complex multiplication.

Modular form 115920.2.a.fb

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 4 q^{11} - 6 q^{13} + 2 q^{17} + O(q^{20})$$ 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 