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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 177450.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.a1 | 177450jn1 | \([1, 1, 0, -416250, -100560000]\) | \(105756712489/3478020\) | \(262308409971562500\) | \([2]\) | \(3870720\) | \(2.1157\) | \(\Gamma_0(N)\)-optimal |
177450.a2 | 177450jn2 | \([1, 1, 0, 133000, -346074750]\) | \(3449795831/688246650\) | \(-51906798819372656250\) | \([2]\) | \(7741440\) | \(2.4622\) |
Rank
sage: E.rank()
The elliptic curves in class 177450.a have rank \(1\).
Complex multiplication
The elliptic curves in class 177450.a do not have complex multiplication.Modular form 177450.2.a.a
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.