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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 19320s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19320.m4 | 19320s1 | \([0, -1, 0, 1500, 23940]\) | \(1457028215984/1851148215\) | \(-473893943040\) | \([4]\) | \(24576\) | \(0.92634\) | \(\Gamma_0(N)\)-optimal |
| 19320.m3 | 19320s2 | \([0, -1, 0, -9080, 239772]\) | \(80859142234084/23148101025\) | \(23703655449600\) | \([2, 2]\) | \(49152\) | \(1.2729\) | |
| 19320.m2 | 19320s3 | \([0, -1, 0, -54160, -4646900]\) | \(8579021289461282/374333754375\) | \(766635528960000\) | \([2]\) | \(98304\) | \(1.6195\) | |
| 19320.m1 | 19320s4 | \([0, -1, 0, -133280, 18770412]\) | \(127847420666360642/17899707105\) | \(36658600151040\) | \([2]\) | \(98304\) | \(1.6195\) |
Rank
sage: E.rank()
The elliptic curves in class 19320s have rank \(1\).
Complex multiplication
The elliptic curves in class 19320s do not have complex multiplication.Modular form 19320.2.a.s
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 Cremona 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 Cremona labels.
