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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 26520g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.t1 | 26520g1 | \([0, 1, 0, -2691, -54630]\) | \(134742996281344/21133125\) | \(338130000\) | \([2]\) | \(16384\) | \(0.64749\) | \(\Gamma_0(N)\)-optimal |
26520.t2 | 26520g2 | \([0, 1, 0, -2436, -65136]\) | \(-6247321674064/3366796875\) | \(-861900000000\) | \([2]\) | \(32768\) | \(0.99407\) |
Rank
sage: E.rank()
The elliptic curves in class 26520g have rank \(0\).
Complex multiplication
The elliptic curves in class 26520g do not have complex multiplication.Modular form 26520.2.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.