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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 43190.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43190.k1 | 43190i1 | \([1, -1, 1, -247, 719]\) | \(1660218096321/773964800\) | \(773964800\) | \([2]\) | \(15680\) | \(0.40005\) | \(\Gamma_0(N)\)-optimal |
43190.k2 | 43190i2 | \([1, -1, 1, 873, 4751]\) | \(73660174154559/53296460000\) | \(-53296460000\) | \([2]\) | \(31360\) | \(0.74662\) |
Rank
sage: E.rank()
The elliptic curves in class 43190.k have rank \(1\).
Complex multiplication
The elliptic curves in class 43190.k do not have complex multiplication.Modular form 43190.2.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.