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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 15030.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15030.g1 | 15030c2 | \([1, -1, 0, -564, -4880]\) | \(735580702683/22311200\) | \(602402400\) | \([2]\) | \(6400\) | \(0.46090\) | |
15030.g2 | 15030c1 | \([1, -1, 0, -84, 208]\) | \(2444008923/855040\) | \(23086080\) | \([2]\) | \(3200\) | \(0.11432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15030.g have rank \(0\).
Complex multiplication
The elliptic curves in class 15030.g do not have complex multiplication.Modular form 15030.2.a.g
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.