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SageMath
E = EllipticCurve("lk1")
E.isogeny_class()
Elliptic curves in class 381150lk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.lk2 | 381150lk1 | \([1, -1, 1, -1475, 9727]\) | \(59319/28\) | \(167412514500\) | \([2]\) | \(414720\) | \(0.84781\) | \(\Gamma_0(N)\)-optimal |
381150.lk1 | 381150lk2 | \([1, -1, 1, -19625, 1062427]\) | \(139798359/98\) | \(585943800750\) | \([2]\) | \(829440\) | \(1.1944\) |
Rank
sage: E.rank()
The elliptic curves in class 381150lk have rank \(0\).
Complex multiplication
The elliptic curves in class 381150lk do not have complex multiplication.Modular form 381150.2.a.lk
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.