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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 37485g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37485.o1 | 37485g1 | \([1, -1, 1, -13313, 442936]\) | \(328509/85\) | \(67513803959385\) | \([2]\) | \(86016\) | \(1.3628\) | \(\Gamma_0(N)\)-optimal |
37485.o2 | 37485g2 | \([1, -1, 1, 32992, 2813752]\) | \(5000211/7225\) | \(-5738673336547725\) | \([2]\) | \(172032\) | \(1.7094\) |
Rank
sage: E.rank()
The elliptic curves in class 37485g have rank \(1\).
Complex multiplication
The elliptic curves in class 37485g do not have complex multiplication.Modular form 37485.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.