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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 302016.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.cp1 | 302016cp1 | \([0, -1, 0, -44716961505, -3643478125206687]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-12172573950834073471671343251456\) | \([]\) | \(812851200\) | \(4.8745\) | \(\Gamma_0(N)\)-optimal |
| 302016.cp2 | 302016cp2 | \([0, -1, 0, 126638321055, 228664054100694753]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-22718079846212799962196180871732002816\) | \([]\) | \(5689958400\) | \(5.8474\) |
Rank
sage: E.rank()
The elliptic curves in class 302016.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 302016.cp do not have complex multiplication.Modular form 302016.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
