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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 200277h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200277.i2 | 200277h1 | \([1, -1, 1, 9049, -1259530]\) | \(4657463/41503\) | \(-730298732604903\) | \([2]\) | \(709632\) | \(1.5333\) | \(\Gamma_0(N)\)-optimal |
200277.i1 | 200277h2 | \([1, -1, 1, -134006, -17396134]\) | \(15124197817/1294139\) | \(22772042298498339\) | \([2]\) | \(1419264\) | \(1.8799\) |
Rank
sage: E.rank()
The elliptic curves in class 200277h have rank \(0\).
Complex multiplication
The elliptic curves in class 200277h do not have complex multiplication.Modular form 200277.2.a.h
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.