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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 414.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414.c1 | 414a4 | \([1, -1, 1, -6935, -36241]\) | \(50591419971625/28422890688\) | \(20720287311552\) | \([6]\) | \(768\) | \(1.2453\) | |
414.c2 | 414a2 | \([1, -1, 1, -5180, -142189]\) | \(21081759765625/57132\) | \(41649228\) | \([2]\) | \(256\) | \(0.69601\) | |
414.c3 | 414a1 | \([1, -1, 1, -320, -2221]\) | \(-4956477625/268272\) | \(-195570288\) | \([2]\) | \(128\) | \(0.34944\) | \(\Gamma_0(N)\)-optimal |
414.c4 | 414a3 | \([1, -1, 1, 1705, -5137]\) | \(752329532375/448524288\) | \(-326974205952\) | \([6]\) | \(384\) | \(0.89874\) |
Rank
sage: E.rank()
The elliptic curves in class 414.c have rank \(0\).
Complex multiplication
The elliptic curves in class 414.c do not have complex multiplication.Modular form 414.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.