Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 323400i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.i1 | 323400i1 | \([0, -1, 0, -18228408, -29748313188]\) | \(355845710666884/2750797665\) | \(5178057511833360000000\) | \([2]\) | \(22118400\) | \(2.9955\) | \(\Gamma_0(N)\)-optimal |
| 323400.i2 | 323400i2 | \([0, -1, 0, -6321408, -68065039188]\) | \(-7420395059282/527349420675\) | \(-1985348223775778400000000\) | \([2]\) | \(44236800\) | \(3.3420\) |
Rank
sage: E.rank()
The elliptic curves in class 323400i have rank \(1\).
Complex multiplication
The elliptic curves in class 323400i do not have complex multiplication.Modular form 323400.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
