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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 9360.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9360.v1 | 9360bj2 | \([0, 0, 0, -122763, -16555718]\) | \(68523370149961/243360\) | \(726669066240\) | \([2]\) | \(30720\) | \(1.4943\) | |
9360.v2 | 9360bj1 | \([0, 0, 0, -7563, -266438]\) | \(-16022066761/998400\) | \(-2981206425600\) | \([2]\) | \(15360\) | \(1.1477\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9360.v have rank \(1\).
Complex multiplication
The elliptic curves in class 9360.v do not have complex multiplication.Modular form 9360.2.a.v
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.