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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 13200.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13200.i1 | 13200bx2 | \([0, -1, 0, -4585208, 4176588912]\) | \(-6663170841705625/850403524608\) | \(-1360645639372800000000\) | \([]\) | \(570240\) | \(2.7889\) | |
13200.i2 | 13200bx1 | \([0, -1, 0, 364792, -13091088]\) | \(3355354844375/1987172352\) | \(-3179475763200000000\) | \([]\) | \(190080\) | \(2.2396\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13200.i have rank \(1\).
Complex multiplication
The elliptic curves in class 13200.i do not have complex multiplication.Modular form 13200.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.