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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 26928ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26928.e1 | 26928ca1 | \([0, 0, 0, -28227, -1824190]\) | \(832972004929/610368\) | \(1822549082112\) | \([2]\) | \(73728\) | \(1.2868\) | \(\Gamma_0(N)\)-optimal |
26928.e2 | 26928ca2 | \([0, 0, 0, -22467, -2590270]\) | \(-420021471169/727634952\) | \(-2172706324512768\) | \([2]\) | \(147456\) | \(1.6334\) |
Rank
sage: E.rank()
The elliptic curves in class 26928ca have rank \(1\).
Complex multiplication
The elliptic curves in class 26928ca do not have complex multiplication.Modular form 26928.2.a.ca
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.