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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1150.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1150.i1 | 1150f2 | \([1, 1, 1, -2913, -61729]\) | \(109348914285625/1472\) | \(36800\) | \([]\) | \(432\) | \(0.43304\) | |
1150.i2 | 1150f1 | \([1, 1, 1, -38, -89]\) | \(243135625/48668\) | \(1216700\) | \([]\) | \(144\) | \(-0.11627\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1150.i have rank \(0\).
Complex multiplication
The elliptic curves in class 1150.i do not have complex multiplication.Modular form 1150.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.