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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 28730.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28730.k1 | 28730n1 | \([1, -1, 0, -2989, 28965]\) | \(611960049/282880\) | \(1365407729920\) | \([2]\) | \(43008\) | \(1.0232\) | \(\Gamma_0(N)\)-optimal |
28730.k2 | 28730n2 | \([1, -1, 0, 10531, 210133]\) | \(26757728271/19536400\) | \(-94298471347600\) | \([2]\) | \(86016\) | \(1.3698\) |
Rank
sage: E.rank()
The elliptic curves in class 28730.k have rank \(1\).
Complex multiplication
The elliptic curves in class 28730.k do not have complex multiplication.Modular form 28730.2.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 LMFDB 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 LMFDB labels.