# Properties

 Label 97020.c Number of curves $2$ Conductor $97020$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 97020.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.c1 97020bn2 $$[0, 0, 0, -337008, -75302332]$$ $$462893166690304/4125$$ $$37721376000$$ $$[]$$ $$373248$$ $$1.6126$$
97020.c2 97020bn1 $$[0, 0, 0, -4368, -92428]$$ $$1007878144/179685$$ $$1643143138560$$ $$[]$$ $$124416$$ $$1.0633$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 97020.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 97020.c do not have complex multiplication.

## Modular form 97020.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} - 5q^{13} - 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 