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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 130130.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130130.v1 | 130130v2 | \([1, -1, 0, -1307500, 575754336]\) | \(51214021297318881/2752750000\) | \(13286998474750000\) | \([2]\) | \(2064384\) | \(2.1609\) | |
130130.v2 | 130130v1 | \([1, -1, 0, -77180, 10053200]\) | \(-10533703412961/2914912000\) | \(-14069723475808000\) | \([2]\) | \(1032192\) | \(1.8143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 130130.v have rank \(0\).
Complex multiplication
The elliptic curves in class 130130.v do not have complex multiplication.Modular form 130130.2.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.