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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 11200i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.cv2 | 11200i1 | \([0, -1, 0, -33, -4063]\) | \(-4/7\) | \(-7168000000\) | \([2]\) | \(5120\) | \(0.57005\) | \(\Gamma_0(N)\)-optimal |
11200.cv1 | 11200i2 | \([0, -1, 0, -4033, -96063]\) | \(3543122/49\) | \(100352000000\) | \([2]\) | \(10240\) | \(0.91662\) |
Rank
sage: E.rank()
The elliptic curves in class 11200i have rank \(1\).
Complex multiplication
The elliptic curves in class 11200i do not have complex multiplication.Modular form 11200.2.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 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.