# Properties

 Label 115920.b Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.b1 115920cx1 $$[0, 0, 0, -23695293, 44395733783]$$ $$-126142795384287538429696/9315359375$$ $$-108654351750000$$ $$[]$$ $$4250880$$ $$2.5895$$ $$\Gamma_0(N)$$-optimal
115920.b2 115920cx2 $$[0, 0, 0, -23456793, 45333186383]$$ $$-122372013839654770813696/5297595236711512175$$ $$-61791150841003078009200$$ $$[]$$ $$12752640$$ $$3.1388$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{11} - q^{13} - 6q^{17} - 2q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 