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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 126350.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.i1 | 126350bx1 | \([1, 0, 1, -14709987576, -686700474702202]\) | \(3830972064521089212269/1001428288\) | \(92017726693909625000000\) | \([2]\) | \(151200000\) | \(4.2186\) | \(\Gamma_0(N)\)-optimal |
126350.i2 | 126350bx2 | \([1, 0, 1, -14708182576, -686877422462202]\) | \(-3829561990703458000109/1958708234387912\) | \(-179978817399870733965765625000\) | \([2]\) | \(302400000\) | \(4.5652\) |
Rank
sage: E.rank()
The elliptic curves in class 126350.i have rank \(0\).
Complex multiplication
The elliptic curves in class 126350.i do not have complex multiplication.Modular form 126350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.