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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 28830k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28830.k2 | 28830k1 | \([1, 1, 0, -13115267, -18313331379]\) | \(-281115640967896441/468084326400\) | \(-415426562698405478400\) | \([2]\) | \(1996800\) | \(2.8521\) | \(\Gamma_0(N)\)-optimal |
28830.k1 | 28830k2 | \([1, 1, 0, -209928067, -1170809725619]\) | \(1152829477932246539641/3188367360\) | \(2829687768380252160\) | \([2]\) | \(3993600\) | \(3.1987\) |
Rank
sage: E.rank()
The elliptic curves in class 28830k have rank \(1\).
Complex multiplication
The elliptic curves in class 28830k do not have complex multiplication.Modular form 28830.2.a.k
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.