Show commands:
SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 33462.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33462.cd1 | 33462cx1 | \([1, -1, 1, -8782863953, -317147097428287]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-92230386992115942263350909824\) | \([]\) | \(47416320\) | \(4.4676\) | \(\Gamma_0(N)\)-optimal |
33462.cd2 | 33462cx2 | \([1, -1, 1, 24873048337, 19904150561794373]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-172132640507838122654187325861624014\) | \([]\) | \(331914240\) | \(5.4406\) |
Rank
sage: E.rank()
The elliptic curves in class 33462.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 33462.cd do not have complex multiplication.Modular form 33462.2.a.cd
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.