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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 69938g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69938.i2 | 69938g1 | \([1, 1, 0, 104179, -4868563]\) | \(24167/16\) | \(-82785636494404624\) | \([]\) | \(887040\) | \(1.9350\) | \(\Gamma_0(N)\)-optimal |
69938.i1 | 69938g2 | \([1, 1, 0, -1819116, -970747312]\) | \(-128667913/4096\) | \(-21193122942567583744\) | \([]\) | \(2661120\) | \(2.4843\) |
Rank
sage: E.rank()
The elliptic curves in class 69938g have rank \(0\).
Complex multiplication
The elliptic curves in class 69938g do not have complex multiplication.Modular form 69938.2.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.