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SageMath
E = EllipticCurve("kj1")
E.isogeny_class()
Elliptic curves in class 381150kj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.kj1 | 381150kj1 | \([1, -1, 1, -4642430, 3830515197]\) | \(4386781853/27216\) | \(68649594227156250000\) | \([2]\) | \(17920000\) | \(2.6443\) | \(\Gamma_0(N)\)-optimal |
| 381150.kj2 | 381150kj2 | \([1, -1, 1, -1919930, 8284525197]\) | \(-310288733/11573604\) | \(-29193239945098195312500\) | \([2]\) | \(35840000\) | \(2.9909\) |
Rank
sage: E.rank()
The elliptic curves in class 381150kj have rank \(1\).
Complex multiplication
The elliptic curves in class 381150kj do not have complex multiplication.Modular form 381150.2.a.kj
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.
