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SageMath
E = EllipticCurve("mc1")
E.isogeny_class()
Elliptic curves in class 176400.mc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.mc1 | 176400iv2 | \([0, 0, 0, -16044315, 24735976650]\) | \(280844088456303/614656\) | \(999664087597056000\) | \([2]\) | \(7077888\) | \(2.7002\) | |
| 176400.mc2 | 176400iv1 | \([0, 0, 0, -991515, 395599050]\) | \(-66282611823/3211264\) | \(-5222734824996864000\) | \([2]\) | \(3538944\) | \(2.3536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.mc have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.mc do not have complex multiplication.Modular form 176400.2.a.mc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
