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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 253920k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253920.k3 | 253920k1 | \([0, -1, 0, -5466, 140616]\) | \(1906624/225\) | \(2131716801600\) | \([2, 2]\) | \(360448\) | \(1.0970\) | \(\Gamma_0(N)\)-optimal |
253920.k1 | 253920k2 | \([0, -1, 0, -84816, 9535656]\) | \(890277128/15\) | \(1136915627520\) | \([2]\) | \(720896\) | \(1.4436\) | |
253920.k4 | 253920k3 | \([0, -1, 0, 7759, 704001]\) | \(85184/405\) | \(-245573775544320\) | \([2]\) | \(720896\) | \(1.4436\) | |
253920.k2 | 253920k4 | \([0, -1, 0, -21336, -1046460]\) | \(14172488/1875\) | \(142114453440000\) | \([2]\) | \(720896\) | \(1.4436\) |
Rank
sage: E.rank()
The elliptic curves in class 253920k have rank \(0\).
Complex multiplication
The elliptic curves in class 253920k do not have complex multiplication.Modular form 253920.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.