# Properties

 Label 62400.bl Number of curves $2$ Conductor $62400$ CM no Rank $1$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.bl1 62400n2 $$[0, -1, 0, -73633, -6864863]$$ $$10779215329/1232010$$ $$5046312960000000$$ $$$$ $$442368$$ $$1.7454$$
62400.bl2 62400n1 $$[0, -1, 0, 6367, -544863]$$ $$6967871/35100$$ $$-143769600000000$$ $$$$ $$221184$$ $$1.3988$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 62400.bl have rank $$1$$.

## Complex multiplication

The elliptic curves in class 62400.bl do not have complex multiplication.

## Modular form 62400.2.a.bl

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} - 4q^{11} - q^{13} - 8q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 