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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 880.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 880.g1 | 880c3 | \([0, 0, 0, -7547, 12986]\) | \(46424454082884/26794860125\) | \(27437936768000\) | \([4]\) | \(2304\) | \(1.2681\) | |
| 880.g2 | 880c2 | \([0, 0, 0, -5047, -137514]\) | \(55537159171536/228765625\) | \(58564000000\) | \([2, 2]\) | \(1152\) | \(0.92153\) | |
| 880.g3 | 880c1 | \([0, 0, 0, -5042, -137801]\) | \(885956203616256/15125\) | \(242000\) | \([2]\) | \(576\) | \(0.57496\) | \(\Gamma_0(N)\)-optimal |
| 880.g4 | 880c4 | \([0, 0, 0, -2627, -269646]\) | \(-1957960715364/29541015625\) | \(-30250000000000\) | \([4]\) | \(2304\) | \(1.2681\) |
Rank
sage: E.rank()
The elliptic curves in class 880.g have rank \(1\).
Complex multiplication
The elliptic curves in class 880.g do not have complex multiplication.Modular form 880.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
