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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 137904ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
137904.de2 | 137904ct1 | \([0, 1, 0, -9351, -261468]\) | \(1171019776/304317\) | \(23502080551248\) | \([2]\) | \(344064\) | \(1.2747\) | \(\Gamma_0(N)\)-optimal |
137904.de1 | 137904ct2 | \([0, 1, 0, -138636, -19912788]\) | \(238481570896/25857\) | \(31950540880128\) | \([2]\) | \(688128\) | \(1.6213\) |
Rank
sage: E.rank()
The elliptic curves in class 137904ct have rank \(1\).
Complex multiplication
The elliptic curves in class 137904ct do not have complex multiplication.Modular form 137904.2.a.ct
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.