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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1938.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1938.i1 | 1938j1 | \([1, 0, 0, -692950, 221979428]\) | \(-36798443442923099464801/2423324873327616\) | \(-2423324873327616\) | \([5]\) | \(22800\) | \(2.0083\) | \(\Gamma_0(N)\)-optimal |
1938.i2 | 1938j2 | \([1, 0, 0, 3598190, 517296968]\) | \(5152001506110026101064159/3096949914094458852996\) | \(-3096949914094458852996\) | \([]\) | \(114000\) | \(2.8130\) |
Rank
sage: E.rank()
The elliptic curves in class 1938.i have rank \(0\).
Complex multiplication
The elliptic curves in class 1938.i do not have complex multiplication.Modular form 1938.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.