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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 84150.gi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84150.gi1 | 84150ga2 | \([1, -1, 1, -40955, -3179703]\) | \(666940371553/37026\) | \(421749281250\) | \([2]\) | \(196608\) | \(1.2960\) | |
84150.gi2 | 84150ga1 | \([1, -1, 1, -2705, -43203]\) | \(192100033/38148\) | \(434529562500\) | \([2]\) | \(98304\) | \(0.94944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.gi have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.gi do not have complex multiplication.Modular form 84150.2.a.gi
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.