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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 930.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 930.n1 | 930n4 | \([1, 0, 0, -635471, -195033699]\) | \(28379906689597370652529/1357352437500\) | \(1357352437500\) | \([2]\) | \(8640\) | \(1.8053\) | |
| 930.n2 | 930n3 | \([1, 0, 0, -39651, -3060495]\) | \(-6894246873502147249/47925198774000\) | \(-47925198774000\) | \([2]\) | \(4320\) | \(1.4587\) | |
| 930.n3 | 930n2 | \([1, 0, 0, -8531, -218655]\) | \(68663623745397169/19216056254400\) | \(19216056254400\) | \([6]\) | \(2880\) | \(1.2560\) | |
| 930.n4 | 930n1 | \([1, 0, 0, 1389, -22239]\) | \(296354077829711/387386634240\) | \(-387386634240\) | \([6]\) | \(1440\) | \(0.90944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 930.n have rank \(0\).
Complex multiplication
The elliptic curves in class 930.n do not have complex multiplication.Modular form 930.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
