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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 82800.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82800.co1 | 82800dd2 | \([0, 0, 0, -419475, -104570030]\) | \(109348914285625/1472\) | \(109884211200\) | \([]\) | \(248832\) | \(1.6755\) | |
| 82800.co2 | 82800dd1 | \([0, 0, 0, -5475, -126110]\) | \(243135625/48668\) | \(3633046732800\) | \([]\) | \(82944\) | \(1.1262\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 82800.co have rank \(1\).
Complex multiplication
The elliptic curves in class 82800.co do not have complex multiplication.Modular form 82800.2.a.co
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
