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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 7200w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7200.p2 | 7200w1 | \([0, 0, 0, 15, 200]\) | \(64/3\) | \(-17496000\) | \([2]\) | \(1536\) | \(0.069550\) | \(\Gamma_0(N)\)-optimal |
7200.p1 | 7200w2 | \([0, 0, 0, -435, 3350]\) | \(195112/9\) | \(419904000\) | \([2]\) | \(3072\) | \(0.41612\) |
Rank
sage: E.rank()
The elliptic curves in class 7200w have rank \(1\).
Complex multiplication
The elliptic curves in class 7200w do not have complex multiplication.Modular form 7200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.