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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 75150p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75150.y2 | 75150p1 | \([1, -1, 0, -1017, 52141]\) | \(-10218313/96192\) | \(-1095687000000\) | \([2]\) | \(147456\) | \(0.99260\) | \(\Gamma_0(N)\)-optimal |
75150.y1 | 75150p2 | \([1, -1, 0, -28017, 1807141]\) | \(213525509833/669336\) | \(7624155375000\) | \([2]\) | \(294912\) | \(1.3392\) |
Rank
sage: E.rank()
The elliptic curves in class 75150p have rank \(1\).
Complex multiplication
The elliptic curves in class 75150p do not have complex multiplication.Modular form 75150.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.