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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 234416.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234416.i1 | 234416i2 | \([0, 1, 0, -433813, -109846269]\) | \(18736316416000/54252653\) | \(26143827446976512\) | \([]\) | \(2239488\) | \(2.0210\) | |
234416.i2 | 234416i1 | \([0, 1, 0, -26133, 1491139]\) | \(4096000000/353717\) | \(170452792659968\) | \([]\) | \(746496\) | \(1.4717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234416.i have rank \(0\).
Complex multiplication
The elliptic curves in class 234416.i do not have complex multiplication.Modular form 234416.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.