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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 380880.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380880.i1 | 380880i1 | \([0, 0, 0, -7592208, -8051865093]\) | \(62200479744/625\) | \(486311218595010000\) | \([2]\) | \(11022336\) | \(2.5529\) | \(\Gamma_0(N)\)-optimal |
380880.i2 | 380880i2 | \([0, 0, 0, -7409703, -8457354702]\) | \(-3613864464/390625\) | \(-4863112185950100000000\) | \([2]\) | \(22044672\) | \(2.8995\) |
Rank
sage: E.rank()
The elliptic curves in class 380880.i have rank \(1\).
Complex multiplication
The elliptic curves in class 380880.i do not have complex multiplication.Modular form 380880.2.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.