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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3536.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3536.g1 | 3536f1 | \([0, 0, 0, -1499, -21622]\) | \(90942871473/3321188\) | \(13603586048\) | \([2]\) | \(2304\) | \(0.71406\) | \(\Gamma_0(N)\)-optimal |
3536.g2 | 3536f2 | \([0, 0, 0, 581, -76950]\) | \(5295319407/627576794\) | \(-2570554548224\) | \([2]\) | \(4608\) | \(1.0606\) |
Rank
sage: E.rank()
The elliptic curves in class 3536.g have rank \(0\).
Complex multiplication
The elliptic curves in class 3536.g do not have complex multiplication.Modular form 3536.2.a.g
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.