# Properties

 Label 26520.bb Number of curves $2$ Conductor $26520$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 26520.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.bb1 26520be2 $$[0, 1, 0, -8285158460, -290175586566192]$$ $$245689277968779868090419995701456/93342399137270122585475925$$ $$23895654179141151381881836800$$ $$$$ $$30965760$$ $$4.4115$$
26520.bb2 26520be1 $$[0, 1, 0, -441593835, -5915392278642]$$ $$-595213448747095198927846967296/600281130562949295663181875$$ $$-9604498089007188730610910000$$ $$$$ $$15482880$$ $$4.0650$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 26520.bb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 26520.bb do not have complex multiplication.

## Modular form 26520.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 2 q^{7} + q^{9} + q^{13} + q^{15} - q^{17} + 4 q^{19} + O(q^{20})$$ ## 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. 