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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7514.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7514.c1 | 7514b3 | \([1, 1, 0, -132801, -18682763]\) | \(-10730978619193/6656\) | \(-160659659264\) | \([]\) | \(30240\) | \(1.4710\) | |
7514.c2 | 7514b2 | \([1, 1, 0, -1306, -36772]\) | \(-10218313/17576\) | \(-424241912744\) | \([]\) | \(10080\) | \(0.92169\) | |
7514.c3 | 7514b1 | \([1, 1, 0, 139, 1087]\) | \(12167/26\) | \(-627576794\) | \([]\) | \(3360\) | \(0.37238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7514.c have rank \(0\).
Complex multiplication
The elliptic curves in class 7514.c do not have complex multiplication.Modular form 7514.2.a.c
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.