# Properties

 Label 35131c Number of curves $3$ Conductor $35131$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 35131c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35131.b3 35131c1 $$[0, -1, 1, 1233, 325]$$ $$32768/19$$ $$-120105897931$$ $$[]$$ $$27090$$ $$0.81543$$ $$\Gamma_0(N)$$-optimal
35131.b2 35131c2 $$[0, -1, 1, -17257, 934070]$$ $$-89915392/6859$$ $$-43358229153091$$ $$[]$$ $$81270$$ $$1.3647$$
35131.b1 35131c3 $$[0, -1, 1, -1422497, 653492395]$$ $$-50357871050752/19$$ $$-120105897931$$ $$[]$$ $$243810$$ $$1.9140$$

## Rank

sage: E.rank()

The elliptic curves in class 35131c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 35131c do not have complex multiplication.

## Modular form 35131.2.a.c

sage: E.q_eigenform(10)

$$q + 2q^{3} - 2q^{4} - 3q^{5} + q^{7} + q^{9} + 3q^{11} - 4q^{12} - 4q^{13} - 6q^{15} + 4q^{16} - 3q^{17} - q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.