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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 19074.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19074.m1 | 19074y3 | \([1, 1, 1, -405827389, -3146903905069]\) | \(306234591284035366263793/1727485056\) | \(41697289735668864\) | \([2]\) | \(3096576\) | \(3.2589\) | |
| 19074.m2 | 19074y2 | \([1, 1, 1, -25364669, -49176438829]\) | \(74768347616680342513/5615307472896\) | \(135539871583242829824\) | \([2, 2]\) | \(1548288\) | \(2.9123\) | |
| 19074.m3 | 19074y4 | \([1, 1, 1, -23700029, -55907577133]\) | \(-60992553706117024753/20624795251201152\) | \(-497832418486740139279488\) | \([2]\) | \(3096576\) | \(3.2589\) | |
| 19074.m4 | 19074y1 | \([1, 1, 1, -1689789, -661874733]\) | \(22106889268753393/4969545596928\) | \(119952749744495788032\) | \([4]\) | \(774144\) | \(2.5657\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19074.m have rank \(1\).
Complex multiplication
The elliptic curves in class 19074.m do not have complex multiplication.Modular form 19074.2.a.m
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.
