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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 363166k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363166.k2 | 363166k1 | \([1, -1, 1, 2820, -14209]\) | \(52734375/32192\) | \(-1514501001152\) | \([2]\) | \(449064\) | \(1.0264\) | \(\Gamma_0(N)\)-optimal |
363166.k1 | 363166k2 | \([1, -1, 1, -11620, -106625]\) | \(3687953625/2024072\) | \(95224250447432\) | \([2]\) | \(898128\) | \(1.3729\) |
Rank
sage: E.rank()
The elliptic curves in class 363166k have rank \(0\).
Complex multiplication
The elliptic curves in class 363166k do not have complex multiplication.Modular form 363166.2.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.