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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 38025.ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.ck1 | 38025cs2 | \([1, -1, 0, -13233492, 18531699291]\) | \(16974593\) | \(15098984458822265625\) | \([2]\) | \(1198080\) | \(2.7423\) | |
38025.ck2 | 38025cs1 | \([1, -1, 0, -875367, 254032416]\) | \(4913\) | \(15098984458822265625\) | \([2]\) | \(599040\) | \(2.3957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38025.ck have rank \(0\).
Complex multiplication
The elliptic curves in class 38025.ck do not have complex multiplication.Modular form 38025.2.a.ck
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.