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SageMath
E = EllipticCurve("gz1")
E.isogeny_class()
Elliptic curves in class 124950.gz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.gz1 | 124950in2 | \([1, 0, 0, -66208213, -197713298833]\) | \(17460273607244690041/918397653311250\) | \(1688258836162738300781250\) | \([2]\) | \(35389440\) | \(3.4059\) | |
124950.gz2 | 124950in1 | \([1, 0, 0, 2698037, -12286580083]\) | \(1181569139409959/36161310937500\) | \(-66474094851342773437500\) | \([2]\) | \(17694720\) | \(3.0593\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124950.gz have rank \(1\).
Complex multiplication
The elliptic curves in class 124950.gz do not have complex multiplication.Modular form 124950.2.a.gz
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.