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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7350p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.k1 | 7350p1 | \([1, 1, 0, -900, -10800]\) | \(-2637114025/6912\) | \(-211680000\) | \([]\) | \(5184\) | \(0.47294\) | \(\Gamma_0(N)\)-optimal |
7350.k2 | 7350p2 | \([1, 1, 0, 1725, -52275]\) | \(18519167975/50331648\) | \(-1541406720000\) | \([]\) | \(15552\) | \(1.0222\) |
Rank
sage: E.rank()
The elliptic curves in class 7350p have rank \(1\).
Complex multiplication
The elliptic curves in class 7350p do not have complex multiplication.Modular form 7350.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.