Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 222530n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222530.bw3 | 222530n1 | \([1, 1, 1, -16190, 15423355]\) | \(-19443408769/4249907200\) | \(-102582428283596800\) | \([2]\) | \(2985984\) | \(1.9434\) | \(\Gamma_0(N)\)-optimal |
| 222530.bw2 | 222530n2 | \([1, 1, 1, -1033470, 400362107]\) | \(5057359576472449/51765560000\) | \(1249494776323640000\) | \([2]\) | \(5971968\) | \(2.2900\) | |
| 222530.bw4 | 222530n3 | \([1, 1, 1, 145650, -415588933]\) | \(14156681599871/3100231750000\) | \(-74832057781615750000\) | \([2]\) | \(8957952\) | \(2.4927\) | |
| 222530.bw1 | 222530n4 | \([1, 1, 1, -7547530, -7757959925]\) | \(1969902499564819009/63690429687500\) | \(1537332141221679687500\) | \([2]\) | \(17915904\) | \(2.8393\) |
Rank
sage: E.rank()
The elliptic curves in class 222530n have rank \(0\).
Complex multiplication
The elliptic curves in class 222530n do not have complex multiplication.Modular form 222530.2.a.n
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
