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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 55440.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.cv1 | 55440ec4 | \([0, 0, 0, -3760707, -2727523006]\) | \(1969902499564819009/63690429687500\) | \(190178604000000000000\) | \([2]\) | \(1990656\) | \(2.6651\) | |
| 55440.cv2 | 55440ec2 | \([0, 0, 0, -514947, 140966786]\) | \(5057359576472449/51765560000\) | \(154571133911040000\) | \([2]\) | \(663552\) | \(2.1158\) | |
| 55440.cv3 | 55440ec1 | \([0, 0, 0, -8067, 5427074]\) | \(-19443408769/4249907200\) | \(-12690154900684800\) | \([2]\) | \(331776\) | \(1.7692\) | \(\Gamma_0(N)\)-optimal |
| 55440.cv4 | 55440ec3 | \([0, 0, 0, 72573, -146192254]\) | \(14156681599871/3100231750000\) | \(-9257242401792000000\) | \([2]\) | \(995328\) | \(2.3185\) |
Rank
sage: E.rank()
The elliptic curves in class 55440.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 55440.cv do not have complex multiplication.Modular form 55440.2.a.cv
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
