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SageMath
E = EllipticCurve("to1")
E.isogeny_class()
Elliptic curves in class 176400.to
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.to1 | 176400cr2 | \([0, 0, 0, -2473275, 1584025450]\) | \(-7620530425/526848\) | \(-115675415850516480000\) | \([]\) | \(5971968\) | \(2.6007\) | |
176400.to2 | 176400cr1 | \([0, 0, 0, 172725, 2246650]\) | \(2595575/1512\) | \(-331976639877120000\) | \([]\) | \(1990656\) | \(2.0514\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.to have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.to do not have complex multiplication.Modular form 176400.2.a.to
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.