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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 68400.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68400.fv1 | 68400fs4 | \([0, 0, 0, -10944075, 13935312250]\) | \(3107086841064961/570\) | \(26593920000000\) | \([2]\) | \(1769472\) | \(2.4117\) | |
| 68400.fv2 | 68400fs3 | \([0, 0, 0, -792075, 144360250]\) | \(1177918188481/488703750\) | \(22800962160000000000\) | \([2]\) | \(1769472\) | \(2.4117\) | |
| 68400.fv3 | 68400fs2 | \([0, 0, 0, -684075, 217692250]\) | \(758800078561/324900\) | \(15158534400000000\) | \([2, 2]\) | \(884736\) | \(2.0651\) | |
| 68400.fv4 | 68400fs1 | \([0, 0, 0, -36075, 4500250]\) | \(-111284641/123120\) | \(-5744286720000000\) | \([2]\) | \(442368\) | \(1.7185\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68400.fv have rank \(0\).
Complex multiplication
The elliptic curves in class 68400.fv do not have complex multiplication.Modular form 68400.2.a.fv
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
