Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 20230q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20230.o4 | 20230q1 | \([1, -1, 1, -1273822, 1032192621]\) | \(-9470133471933009/13576123187200\) | \(-327694610183539916800\) | \([2]\) | \(774144\) | \(2.6287\) | \(\Gamma_0(N)\)-optimal |
| 20230.o3 | 20230q2 | \([1, -1, 1, -24948702, 47946334829]\) | \(71149857462630609489/41907496960000\) | \(1011545099489290240000\) | \([2, 2]\) | \(1548288\) | \(2.9752\) | |
| 20230.o2 | 20230q3 | \([1, -1, 1, -29572702, 28936146029]\) | \(118495863754334673489/53596139570691200\) | \(1293680517021189217692800\) | \([2]\) | \(3096576\) | \(3.3218\) | |
| 20230.o1 | 20230q4 | \([1, -1, 1, -399122782, 3069177526381]\) | \(291306206119284545407569/101150000000\) | \(2441515104350000000\) | \([2]\) | \(3096576\) | \(3.3218\) |
Rank
sage: E.rank()
The elliptic curves in class 20230q have rank \(0\).
Complex multiplication
The elliptic curves in class 20230q do not have complex multiplication.Modular form 20230.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
