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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 213444g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.h1 | 213444g1 | \([0, 0, 0, -920068149, -10856547853459]\) | \(-35431687725461248/440311012911\) | \(-1070413086602164506430377456\) | \([]\) | \(149299200\) | \(3.9970\) | \(\Gamma_0(N)\)-optimal |
213444.h2 | 213444g2 | \([0, 0, 0, 3200468271, -55480942996171]\) | \(1491325446082364672/1410025768453071\) | \(-3427827128420058983696481912816\) | \([]\) | \(447897600\) | \(4.5463\) |
Rank
sage: E.rank()
The elliptic curves in class 213444g have rank \(1\).
Complex multiplication
The elliptic curves in class 213444g do not have complex multiplication.Modular form 213444.2.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.