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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 24150i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.n2 | 24150i1 | \([1, 1, 0, -208875, -16927875]\) | \(64500981545311921/29485596672000\) | \(460712448000000000\) | \([2]\) | \(414720\) | \(2.0842\) | \(\Gamma_0(N)\)-optimal |
24150.n1 | 24150i2 | \([1, 1, 0, -1680875, 826528125]\) | \(33613237452390629041/532385784000000\) | \(8318527875000000000\) | \([2]\) | \(829440\) | \(2.4308\) |
Rank
sage: E.rank()
The elliptic curves in class 24150i have rank \(0\).
Complex multiplication
The elliptic curves in class 24150i do not have complex multiplication.Modular form 24150.2.a.i
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.