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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3536.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3536.k1 | 3536a2 | \([0, -1, 0, -2192, -7840]\) | \(569001644066/313788397\) | \(642638637056\) | \([2]\) | \(3840\) | \(0.95630\) | |
3536.k2 | 3536a1 | \([0, -1, 0, -1672, -25728]\) | \(505117359652/830297\) | \(850224128\) | \([2]\) | \(1920\) | \(0.60972\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3536.k have rank \(1\).
Complex multiplication
The elliptic curves in class 3536.k do not have complex multiplication.Modular form 3536.2.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.