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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 300713.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 300713.n1 | 300713n4 | \([1, -1, 0, -1604171, -781630200]\) | \(82483294977/17\) | \(94093314514073\) | \([2]\) | \(1990656\) | \(2.0685\) | |
| 300713.n2 | 300713n2 | \([1, -1, 0, -100606, -12105633]\) | \(20346417/289\) | \(1599586346739241\) | \([2, 2]\) | \(995328\) | \(1.7220\) | |
| 300713.n3 | 300713n3 | \([1, -1, 0, -12161, -32713318]\) | \(-35937/83521\) | \(-462280454207640649\) | \([2]\) | \(1990656\) | \(2.0685\) | |
| 300713.n4 | 300713n1 | \([1, -1, 0, -12161, 223600]\) | \(35937/17\) | \(94093314514073\) | \([2]\) | \(497664\) | \(1.3754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 300713.n have rank \(1\).
Complex multiplication
The elliptic curves in class 300713.n do not have complex multiplication.Modular form 300713.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
