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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 35904.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35904.n1 | 35904s4 | \([0, -1, 0, -25729, 1595905]\) | \(28742820444292/24805737\) | \(1625668780032\) | \([2]\) | \(73728\) | \(1.2695\) | |
35904.n2 | 35904s3 | \([0, -1, 0, -16929, -833247]\) | \(8187726931492/99379467\) | \(6512932749312\) | \([2]\) | \(73728\) | \(1.2695\) | |
35904.n3 | 35904s2 | \([0, -1, 0, -1969, 13489]\) | \(51553893328/25492401\) | \(417667497984\) | \([2, 2]\) | \(36864\) | \(0.92291\) | |
35904.n4 | 35904s1 | \([0, -1, 0, 451, 1389]\) | \(9885304832/6720219\) | \(-6881504256\) | \([2]\) | \(18432\) | \(0.57633\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35904.n have rank \(0\).
Complex multiplication
The elliptic curves in class 35904.n do not have complex multiplication.Modular form 35904.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.