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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1104.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1104.g1 | 1104h3 | \([0, 1, 0, -3952, -96940]\) | \(1666957239793/301806\) | \(1236197376\) | \([2]\) | \(768\) | \(0.74816\) | |
| 1104.g2 | 1104h4 | \([0, 1, 0, -1712, 25812]\) | \(135559106353/5037138\) | \(20632117248\) | \([4]\) | \(768\) | \(0.74816\) | |
| 1104.g3 | 1104h2 | \([0, 1, 0, -272, -1260]\) | \(545338513/171396\) | \(702038016\) | \([2, 2]\) | \(384\) | \(0.40159\) | |
| 1104.g4 | 1104h1 | \([0, 1, 0, 48, -108]\) | \(2924207/3312\) | \(-13565952\) | \([2]\) | \(192\) | \(0.055014\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1104.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1104.g do not have complex multiplication.Modular form 1104.2.a.g
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.
