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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 142912.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142912.i1 | 142912bi1 | \([0, 1, 0, -1492492, 701307210]\) | \(5744868139459169941312/54849179\) | \(3510347456\) | \([2]\) | \(829440\) | \(1.8656\) | \(\Gamma_0(N)\)-optimal |
| 142912.i2 | 142912bi2 | \([0, 1, 0, -1492457, 701341783]\) | \(-89757249770050982848/8770940049487\) | \(-35925770442698752\) | \([2]\) | \(1658880\) | \(2.2122\) |
Rank
sage: E.rank()
The elliptic curves in class 142912.i have rank \(1\).
Complex multiplication
The elliptic curves in class 142912.i do not have complex multiplication.Modular form 142912.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
