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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 110400.ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110400.ch1 | 110400z4 | \([0, -1, 0, -105633, 13039137]\) | \(63649751618/1164375\) | \(2384640000000000\) | \([2]\) | \(589824\) | \(1.7455\) | |
110400.ch2 | 110400z2 | \([0, -1, 0, -13633, -300863]\) | \(273671716/119025\) | \(121881600000000\) | \([2, 2]\) | \(294912\) | \(1.3989\) | |
110400.ch3 | 110400z1 | \([0, -1, 0, -11633, -478863]\) | \(680136784/345\) | \(88320000000\) | \([2]\) | \(147456\) | \(1.0524\) | \(\Gamma_0(N)\)-optimal |
110400.ch4 | 110400z3 | \([0, -1, 0, 46367, -2280863]\) | \(5382838942/4197615\) | \(-8596715520000000\) | \([2]\) | \(589824\) | \(1.7455\) |
Rank
sage: E.rank()
The elliptic curves in class 110400.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 110400.ch do not have complex multiplication.Modular form 110400.2.a.ch
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.