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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 43758k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43758.q2 | 43758k1 | \([1, -1, 1, -11450, 333289]\) | \(8433606238875/2484248624\) | \(48897465666192\) | \([2]\) | \(116736\) | \(1.3325\) | \(\Gamma_0(N)\)-optimal |
43758.q1 | 43758k2 | \([1, -1, 1, -167510, 26426521]\) | \(26409015101734875/3994998436\) | \(78633554215788\) | \([2]\) | \(233472\) | \(1.6791\) |
Rank
sage: E.rank()
The elliptic curves in class 43758k have rank \(0\).
Complex multiplication
The elliptic curves in class 43758k do not have complex multiplication.Modular form 43758.2.a.k
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.