# Properties

 Label 92400.ei Number of curves $2$ Conductor $92400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ei1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.ei

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ei1 92400ct2 $$[0, 1, 0, -11208, 351588]$$ $$77860436/17787$$ $$35574000000000$$ $$$$ $$184320$$ $$1.3127$$
92400.ei2 92400ct1 $$[0, 1, 0, -3708, -83412]$$ $$11279504/693$$ $$346500000000$$ $$$$ $$92160$$ $$0.96614$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 92400.ei have rank $$1$$.

## Complex multiplication

The elliptic curves in class 92400.ei do not have complex multiplication.

## Modular form 92400.2.a.ei

sage: E.q_eigenform(10)

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