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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 930.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
930.i1 | 930i2 | \([1, 0, 1, -523, -4642]\) | \(-15777367606441/3574920\) | \(-3574920\) | \([]\) | \(360\) | \(0.24960\) | |
930.i2 | 930i1 | \([1, 0, 1, 2, -22]\) | \(1685159/209250\) | \(-209250\) | \([3]\) | \(120\) | \(-0.29970\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 930.i have rank \(0\).
Complex multiplication
The elliptic curves in class 930.i do not have complex multiplication.Modular form 930.2.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.