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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 57330bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.a1 | 57330bg1 | \([1, -1, 0, -154800, -23167040]\) | \(13945313143/162240\) | \(4772740546566720\) | \([2]\) | \(688128\) | \(1.8209\) | \(\Gamma_0(N)\)-optimal |
57330.a2 | 57330bg2 | \([1, -1, 0, -31320, -59198504]\) | \(-115501303/51409800\) | \(-1512362160693329400\) | \([2]\) | \(1376256\) | \(2.1675\) |
Rank
sage: E.rank()
The elliptic curves in class 57330bg have rank \(1\).
Complex multiplication
The elliptic curves in class 57330bg do not have complex multiplication.Modular form 57330.2.a.bg
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.