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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 43190.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43190.g1 | 43190s2 | \([1, -1, 1, -1270782, -2412118701]\) | \(-226953328047600468451761/2382836194386693393110\) | \(-2382836194386693393110\) | \([]\) | \(6108144\) | \(2.7840\) | |
43190.g2 | 43190s1 | \([1, -1, 1, -137832, 20026539]\) | \(-289581579184798874961/5081260310000000\) | \(-5081260310000000\) | \([7]\) | \(872592\) | \(1.8111\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43190.g have rank \(1\).
Complex multiplication
The elliptic curves in class 43190.g do not have complex multiplication.Modular form 43190.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.