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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 440.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 440.c1 | 440c3 | \([0, 0, 0, -7547, -12986]\) | \(46424454082884/26794860125\) | \(27437936768000\) | \([2]\) | \(1152\) | \(1.2681\) | |
| 440.c2 | 440c2 | \([0, 0, 0, -5047, 137514]\) | \(55537159171536/228765625\) | \(58564000000\) | \([2, 2]\) | \(576\) | \(0.92153\) | |
| 440.c3 | 440c1 | \([0, 0, 0, -5042, 137801]\) | \(885956203616256/15125\) | \(242000\) | \([4]\) | \(288\) | \(0.57496\) | \(\Gamma_0(N)\)-optimal |
| 440.c4 | 440c4 | \([0, 0, 0, -2627, 269646]\) | \(-1957960715364/29541015625\) | \(-30250000000000\) | \([4]\) | \(1152\) | \(1.2681\) |
Rank
sage: E.rank()
The elliptic curves in class 440.c have rank \(0\).
Complex multiplication
The elliptic curves in class 440.c do not have complex multiplication.Modular form 440.2.a.c
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.
