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SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 137280.gu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
137280.gu1 | 137280eq2 | \([0, 1, 0, -1032495425, -12770033030625]\) | \(464352938845529653759213009/2445173327025000\) | \(640987516639641600000\) | \([2]\) | \(30965760\) | \(3.6092\) | |
137280.gu2 | 137280eq1 | \([0, 1, 0, -64495425, -199778630625]\) | \(-113180217375258301213009/260161419375000000\) | \(-68199755120640000000000\) | \([2]\) | \(15482880\) | \(3.2626\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 137280.gu have rank \(0\).
Complex multiplication
The elliptic curves in class 137280.gu do not have complex multiplication.Modular form 137280.2.a.gu
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.