# Properties

 Label 4235.c Number of curves $3$ Conductor $4235$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 4235.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4235.c1 4235b3 $$[0, 1, 1, -15891, 801301]$$ $$-250523582464/13671875$$ $$-24220560546875$$ $$[]$$ $$8100$$ $$1.3264$$
4235.c2 4235b1 $$[0, 1, 1, -161, -929]$$ $$-262144/35$$ $$-62004635$$ $$[]$$ $$900$$ $$0.22780$$ $$\Gamma_0(N)$$-optimal
4235.c3 4235b2 $$[0, 1, 1, 1049, 2580]$$ $$71991296/42875$$ $$-75955677875$$ $$[]$$ $$2700$$ $$0.77710$$

## Rank

sage: E.rank()

The elliptic curves in class 4235.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4235.c do not have complex multiplication.

## Modular form4235.2.a.c

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} - q^{5} - q^{7} - 2q^{9} - 2q^{12} - 5q^{13} - q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 