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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 14450w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14450.v2 | 14450w1 | \([1, 0, 0, -18449188, 30499006992]\) | \(1841373668746009/31443200\) | \(11858787649700000000\) | \([2]\) | \(1105920\) | \(2.7895\) | \(\Gamma_0(N)\)-optimal |
| 14450.v3 | 14450w2 | \([1, 0, 0, -17871188, 32499464992]\) | \(-1673672305534489/241375690000\) | \(-91034724567150156250000\) | \([2]\) | \(2211840\) | \(3.1361\) | |
| 14450.v1 | 14450w3 | \([1, 0, 0, -30117563, -12516150383]\) | \(8010684753304969/4456448000000\) | \(1680747204608000000000000\) | \([2]\) | \(3317760\) | \(3.3388\) | |
| 14450.v4 | 14450w4 | \([1, 0, 0, 117850437, -99077430383]\) | \(479958568556831351/289000000000000\) | \(-108996210015625000000000000\) | \([2]\) | \(6635520\) | \(3.6854\) |
Rank
sage: E.rank()
The elliptic curves in class 14450w have rank \(0\).
Complex multiplication
The elliptic curves in class 14450w do not have complex multiplication.Modular form 14450.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
