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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7440.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7440.k1 | 7440l2 | \([0, -1, 0, -8360, 297072]\) | \(-15777367606441/3574920\) | \(-14642872320\) | \([]\) | \(8640\) | \(0.94275\) | |
7440.k2 | 7440l1 | \([0, -1, 0, 40, 1392]\) | \(1685159/209250\) | \(-857088000\) | \([]\) | \(2880\) | \(0.39345\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7440.k have rank \(1\).
Complex multiplication
The elliptic curves in class 7440.k do not have complex multiplication.Modular form 7440.2.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 LMFDB 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 LMFDB labels.