# Properties

 Label 97461.v Number of curves $4$ Conductor $97461$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 97461.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.v1 97461k4 $$[1, -1, 0, -10915641, -13878310608]$$ $$1677087406638588673/4641$$ $$398040567561$$ $$$$ $$1966080$$ $$2.3442$$
97461.v2 97461k2 $$[1, -1, 0, -682236, -216714933]$$ $$409460675852593/21538881$$ $$1847306274050601$$ $$[2, 2]$$ $$983040$$ $$1.9976$$
97461.v3 97461k3 $$[1, -1, 0, -644751, -241612470]$$ $$-345608484635233/94427721297$$ $$-8098699370512778937$$ $$$$ $$1966080$$ $$2.3442$$
97461.v4 97461k1 $$[1, -1, 0, -44991, -2982960]$$ $$117433042273/22801233$$ $$1955573308427193$$ $$$$ $$491520$$ $$1.6511$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 97461.v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 97461.v do not have complex multiplication.

## Modular form 97461.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + 2q^{5} - 3q^{8} + 2q^{10} - 4q^{11} - q^{13} - q^{16} + q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 