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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 185130.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185130.k1 | 185130ea2 | \([1, -1, 0, -748710, 246842316]\) | \(35940267099001/448014600\) | \(578596505544347400\) | \([2]\) | \(4423680\) | \(2.2180\) | |
185130.k2 | 185130ea1 | \([1, -1, 0, -8190, 10024020]\) | \(-47045881/33570240\) | \(-43354889671642560\) | \([2]\) | \(2211840\) | \(1.8714\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185130.k have rank \(0\).
Complex multiplication
The elliptic curves in class 185130.k do not have complex multiplication.Modular form 185130.2.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.