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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 13552g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13552.x2 | 13552g1 | \([0, -1, 0, -1492, -36672]\) | \(-810448/847\) | \(-384131114752\) | \([2]\) | \(15360\) | \(0.91809\) | \(\Gamma_0(N)\)-optimal |
13552.x1 | 13552g2 | \([0, -1, 0, -28112, -1804240]\) | \(1354435492/539\) | \(977788292096\) | \([2]\) | \(30720\) | \(1.2647\) |
Rank
sage: E.rank()
The elliptic curves in class 13552g have rank \(1\).
Complex multiplication
The elliptic curves in class 13552g do not have complex multiplication.Modular form 13552.2.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 Cremona 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 Cremona labels.