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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 23400.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23400.k1 | 23400bc2 | \([0, 0, 0, -1275, 11750]\) | \(530604/169\) | \(73008000000\) | \([2]\) | \(16384\) | \(0.78828\) | |
23400.k2 | 23400bc1 | \([0, 0, 0, 225, 1250]\) | \(11664/13\) | \(-1404000000\) | \([2]\) | \(8192\) | \(0.44170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23400.k have rank \(1\).
Complex multiplication
The elliptic curves in class 23400.k do not have complex multiplication.Modular form 23400.2.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.