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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 254320g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254320.g1 | 254320g1 | \([0, 1, 0, -60830261, -182631793565]\) | \(-251784668965666816/353546875\) | \(-34954289520832000000\) | \([]\) | \(30357504\) | \(3.0224\) | \(\Gamma_0(N)\)-optimal |
254320.g2 | 254320g2 | \([0, 1, 0, -44646261, -281910923165]\) | \(-99546392709922816/289614925147075\) | \(-28633498579629498206924800\) | \([]\) | \(91072512\) | \(3.5717\) |
Rank
sage: E.rank()
The elliptic curves in class 254320g have rank \(0\).
Complex multiplication
The elliptic curves in class 254320g do not have complex multiplication.Modular form 254320.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.