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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 265200.fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 265200.fm1 | 265200fm1 | \([0, 1, 0, -7025408, -7158898812]\) | \(2396726313900986596/4154072495625\) | \(66465159930000000000\) | \([2]\) | \(8847360\) | \(2.6975\) | \(\Gamma_0(N)\)-optimal |
| 265200.fm2 | 265200fm2 | \([0, 1, 0, -4828408, -11715476812]\) | \(-389032340685029858/1627263833203125\) | \(-52072442662500000000000\) | \([2]\) | \(17694720\) | \(3.0441\) |
Rank
sage: E.rank()
The elliptic curves in class 265200.fm have rank \(0\).
Complex multiplication
The elliptic curves in class 265200.fm do not have complex multiplication.Modular form 265200.2.a.fm
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.
