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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4830q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.o3 | 4830q1 | \([1, 0, 1, -220203, 39754006]\) | \(1180838681727016392361/692428800000\) | \(692428800000\) | \([2]\) | \(30720\) | \(1.5961\) | \(\Gamma_0(N)\)-optimal |
4830.o2 | 4830q2 | \([1, 0, 1, -221483, 39268118]\) | \(1201550658189465626281/28577902500000000\) | \(28577902500000000\) | \([2, 2]\) | \(61440\) | \(1.9427\) | |
4830.o1 | 4830q3 | \([1, 0, 1, -491963, -75523594]\) | \(13167998447866683762601/5158996582031250000\) | \(5158996582031250000\) | \([2]\) | \(122880\) | \(2.2892\) | |
4830.o4 | 4830q4 | \([1, 0, 1, 28517, 122968118]\) | \(2564821295690373719/6533572090396050000\) | \(-6533572090396050000\) | \([4]\) | \(122880\) | \(2.2892\) |
Rank
sage: E.rank()
The elliptic curves in class 4830q have rank \(1\).
Complex multiplication
The elliptic curves in class 4830q do not have complex multiplication.Modular form 4830.2.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.