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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 120384.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120384.cd1 | 120384bg2 | \([0, 0, 0, -1082280, 433368722]\) | \(-3004935183806464000/2037123\) | \(-95044010688\) | \([]\) | \(622080\) | \(1.8561\) | |
| 120384.cd2 | 120384bg1 | \([0, 0, 0, -13080, 620714]\) | \(-5304438784000/497763387\) | \(-23223648583872\) | \([]\) | \(207360\) | \(1.3067\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 120384.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 120384.cd do not have complex multiplication.Modular form 120384.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
