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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 85800.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85800.cp1 | 85800bh2 | \([0, 1, 0, -590408, -169143312]\) | \(711264560340098/26281975005\) | \(841023200160000000\) | \([2]\) | \(1327104\) | \(2.2086\) | |
| 85800.cp2 | 85800bh1 | \([0, 1, 0, 14592, -9423312]\) | \(21474271004/2412470775\) | \(-38599532400000000\) | \([2]\) | \(663552\) | \(1.8621\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85800.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 85800.cp do not have complex multiplication.Modular form 85800.2.a.cp
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.
