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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 277350l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.l2 | 277350l1 | \([1, 1, 0, 16848050, -43454103500]\) | \(42838260499/90882048\) | \(-1122067226649696000000000\) | \([2]\) | \(49674240\) | \(3.2991\) | \(\Gamma_0(N)\)-optimal |
277350.l1 | 277350l2 | \([1, 1, 0, -131071950, -470203303500]\) | \(20170293914861/3938458752\) | \(48625835204889560250000000\) | \([2]\) | \(99348480\) | \(3.6456\) |
Rank
sage: E.rank()
The elliptic curves in class 277350l have rank \(1\).
Complex multiplication
The elliptic curves in class 277350l do not have complex multiplication.Modular form 277350.2.a.l
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.