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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 14450.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.w1 | 14450bk2 | \([1, 0, 0, -21967763, 39628654267]\) | \(-297756989/2\) | \(-7874976173628906250\) | \([]\) | \(1040400\) | \(2.8077\) | |
14450.w2 | 14450bk1 | \([1, 0, 0, -16513, -916983]\) | \(-882216989/131072\) | \(-73984000000000\) | \([]\) | \(61200\) | \(1.3911\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14450.w have rank \(1\).
Complex multiplication
The elliptic curves in class 14450.w 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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 17 \\ 17 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.