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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 760.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
760.c1 | 760e4 | \([0, 0, 0, -2027, 35126]\) | \(899466517764/95\) | \(97280\) | \([2]\) | \(256\) | \(0.38532\) | |
760.c2 | 760e3 | \([0, 0, 0, -227, -434]\) | \(1263284964/651605\) | \(667243520\) | \([2]\) | \(256\) | \(0.38532\) | |
760.c3 | 760e2 | \([0, 0, 0, -127, 546]\) | \(884901456/9025\) | \(2310400\) | \([2, 2]\) | \(128\) | \(0.038746\) | |
760.c4 | 760e1 | \([0, 0, 0, -2, 21]\) | \(-55296/11875\) | \(-190000\) | \([4]\) | \(64\) | \(-0.30783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 760.c have rank \(1\).
Complex multiplication
The elliptic curves in class 760.c do not have complex multiplication.Modular form 760.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.