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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 352800.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.k1 | 352800k2 | \([0, 0, 0, -532875, 143631250]\) | \(195112/9\) | \(771895089000000000\) | \([2]\) | \(5529600\) | \(2.1938\) | |
352800.k2 | 352800k1 | \([0, 0, 0, 18375, 8575000]\) | \(64/3\) | \(-32162295375000000\) | \([2]\) | \(2764800\) | \(1.8472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 352800.k have rank \(1\).
Complex multiplication
The elliptic curves in class 352800.k do not have complex multiplication.Modular form 352800.2.a.k
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.