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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 90480i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90480.p2 | 90480i1 | \([0, -1, 0, -638515, 189816850]\) | \(1799358592611632982016/70654089111328125\) | \(1130465425781250000\) | \([2]\) | \(1351680\) | \(2.2312\) | \(\Gamma_0(N)\)-optimal |
90480.p1 | 90480i2 | \([0, -1, 0, -1654140, -562964400]\) | \(1955243274404098311376/595640841502078125\) | \(152484055424532000000\) | \([2]\) | \(2703360\) | \(2.5777\) |
Rank
sage: E.rank()
The elliptic curves in class 90480i have rank \(1\).
Complex multiplication
The elliptic curves in class 90480i do not have complex multiplication.Modular form 90480.2.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 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.