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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 61710g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.b2 | 61710g1 | \([1, 1, 0, 1692, -70308]\) | \(302111711/1404540\) | \(-2488228286940\) | \([2]\) | \(115200\) | \(1.0609\) | \(\Gamma_0(N)\)-optimal |
61710.b1 | 61710g2 | \([1, 1, 0, -18878, -897222]\) | \(420021471169/50191650\) | \(88917569665650\) | \([2]\) | \(230400\) | \(1.4075\) |
Rank
sage: E.rank()
The elliptic curves in class 61710g have rank \(1\).
Complex multiplication
The elliptic curves in class 61710g do not have complex multiplication.Modular form 61710.2.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.