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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 141570ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.bd2 | 141570ei1 | \([1, -1, 0, -57195, -5526779]\) | \(-16022066761/998400\) | \(-1289401620249600\) | \([2]\) | \(819200\) | \(1.6535\) | \(\Gamma_0(N)\)-optimal |
141570.bd1 | 141570ei2 | \([1, -1, 0, -928395, -344075099]\) | \(68523370149961/243360\) | \(314291644935840\) | \([2]\) | \(1638400\) | \(2.0001\) |
Rank
sage: E.rank()
The elliptic curves in class 141570ei have rank \(0\).
Complex multiplication
The elliptic curves in class 141570ei do not have complex multiplication.Modular form 141570.2.a.ei
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 Cremona 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 Cremona labels.