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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 37030.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37030.g1 | 37030e2 | \([1, -1, 0, -27854065, 55700840631]\) | \(1326902312327103/23925781250\) | \(43093984576019042968750\) | \([2]\) | \(3815424\) | \(3.1386\) | |
37030.g2 | 37030e1 | \([1, -1, 0, -27732395, 56218935825]\) | \(1309589935642143/437500\) | \(788004289390062500\) | \([2]\) | \(1907712\) | \(2.7920\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37030.g have rank \(1\).
Complex multiplication
The elliptic curves in class 37030.g do not have complex multiplication.Modular form 37030.2.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.