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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 44352.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.z1 | 44352dn4 | \([0, 0, 0, -130476, -18132784]\) | \(1285429208617/614922\) | \(117513424207872\) | \([2]\) | \(196608\) | \(1.6547\) | |
| 44352.z2 | 44352dn3 | \([0, 0, 0, -72876, 7446224]\) | \(223980311017/4278582\) | \(817649753260032\) | \([2]\) | \(196608\) | \(1.6547\) | |
| 44352.z3 | 44352dn2 | \([0, 0, 0, -9516, -182320]\) | \(498677257/213444\) | \(40789783609344\) | \([2, 2]\) | \(98304\) | \(1.3081\) | |
| 44352.z4 | 44352dn1 | \([0, 0, 0, 2004, -21040]\) | \(4657463/3696\) | \(-706316599296\) | \([2]\) | \(49152\) | \(0.96154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44352.z have rank \(1\).
Complex multiplication
The elliptic curves in class 44352.z do not have complex multiplication.Modular form 44352.2.a.z
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.
