# Properties

 Label 23275.l Number of curves $3$ Conductor $23275$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 23275.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23275.l1 23275i3 $$[0, 1, 1, -942433, 351832919]$$ $$-50357871050752/19$$ $$-34927046875$$ $$[]$$ $$122472$$ $$1.8111$$
23275.l2 23275i2 $$[0, 1, 1, -11433, 496794]$$ $$-89915392/6859$$ $$-12608663921875$$ $$[]$$ $$40824$$ $$1.2618$$
23275.l3 23275i1 $$[0, 1, 1, 817, 669]$$ $$32768/19$$ $$-34927046875$$ $$[]$$ $$13608$$ $$0.71250$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 23275.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 23275.l do not have complex multiplication.

## Modular form 23275.2.a.l

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{4} + q^{9} + 3q^{11} + 4q^{12} - 4q^{13} + 4q^{16} - 3q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 