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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 75504ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75504.bk2 | 75504ct1 | \([0, 1, 0, -645, 5454]\) | \(1048576/117\) | \(3316362192\) | \([2]\) | \(61440\) | \(0.55985\) | \(\Gamma_0(N)\)-optimal |
| 75504.bk1 | 75504ct2 | \([0, 1, 0, -2460, -41736]\) | \(3631696/507\) | \(229934445312\) | \([2]\) | \(122880\) | \(0.90642\) |
Rank
sage: E.rank()
The elliptic curves in class 75504ct have rank \(0\).
Complex multiplication
The elliptic curves in class 75504ct do not have complex multiplication.Modular form 75504.2.a.ct
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.
