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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 48510p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48510.i2 | 48510p1 | \([1, -1, 0, -94462650, 174845689780]\) | \(3168795413730153943/1384979642449920\) | \(40743025737735525279989760\) | \([2]\) | \(15482880\) | \(3.6101\) | \(\Gamma_0(N)\)-optimal |
48510.i1 | 48510p2 | \([1, -1, 0, -734582970, -7542572912204]\) | \(1490171974311284012503/26891921826316800\) | \(791100626698500685024550400\) | \([2]\) | \(30965760\) | \(3.9567\) |
Rank
sage: E.rank()
The elliptic curves in class 48510p have rank \(1\).
Complex multiplication
The elliptic curves in class 48510p do not have complex multiplication.Modular form 48510.2.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.