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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 14157k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14157.d2 | 14157k1 | \([1, -1, 1, 2155, 48084]\) | \(857375/1287\) | \(-1662119276103\) | \([2]\) | \(15360\) | \(1.0303\) | \(\Gamma_0(N)\)-optimal |
14157.d1 | 14157k2 | \([1, -1, 1, -14180, 492396]\) | \(244140625/61347\) | \(79227685494243\) | \([2]\) | \(30720\) | \(1.3769\) |
Rank
sage: E.rank()
The elliptic curves in class 14157k have rank \(1\).
Complex multiplication
The elliptic curves in class 14157k do not have complex multiplication.Modular form 14157.2.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 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.