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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 119952dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.n1 | 119952dh1 | \([0, 0, 0, -22344, 1285564]\) | \(-1517101056/17\) | \(-13824228096\) | \([]\) | \(207360\) | \(1.0988\) | \(\Gamma_0(N)\)-optimal |
119952.n2 | 119952dh2 | \([0, 0, 0, -10584, 2630124]\) | \(-221184/4913\) | \(-2912502199493376\) | \([]\) | \(622080\) | \(1.6481\) |
Rank
sage: E.rank()
The elliptic curves in class 119952dh have rank \(2\).
Complex multiplication
The elliptic curves in class 119952dh do not have complex multiplication.Modular form 119952.2.a.dh
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.