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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 377377g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
377377.g1 | 377377g1 | \([0, 1, 1, -10703, 638668]\) | \(-28094464000/20657483\) | \(-99709724861747\) | \([]\) | \(774144\) | \(1.3855\) | \(\Gamma_0(N)\)-optimal |
377377.g2 | 377377g2 | \([0, 1, 1, 87317, -9883779]\) | \(15252992000000/17621717267\) | \(-85056663499811003\) | \([]\) | \(2322432\) | \(1.9349\) |
Rank
sage: E.rank()
The elliptic curves in class 377377g have rank \(1\).
Complex multiplication
The elliptic curves in class 377377g do not have complex multiplication.Modular form 377377.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.