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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 377520.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.cn1 | 377520cn6 | \([0, -1, 0, -11516876840, -475714832614800]\) | \(23281546263261052473907201/1115400\) | \(8093692474982400\) | \([2]\) | \(176947200\) | \(3.9431\) | |
| 377520.cn2 | 377520cn4 | \([0, -1, 0, -719804840, -7432863488400]\) | \(5683972151443376419201/1244117160000\) | \(9027704586595368960000\) | \([2, 2]\) | \(88473600\) | \(3.5965\) | |
| 377520.cn3 | 377520cn5 | \([0, -1, 0, -717249320, -7488263073168]\) | \(-5623647484692626737921/84122230603125000\) | \(-610417307523083174400000000\) | \([2]\) | \(176947200\) | \(3.9431\) | |
| 377520.cn4 | 377520cn2 | \([0, -1, 0, -45147560, -115260766608]\) | \(1402524686897642881/20523074457600\) | \(148921869554402564505600\) | \([2, 2]\) | \(44236800\) | \(3.2499\) | |
| 377520.cn5 | 377520cn1 | \([0, -1, 0, -5498280, 2164541040]\) | \(2533309721804161/1187575234560\) | \(8617418629580178063360\) | \([2]\) | \(22118400\) | \(2.9033\) | \(\Gamma_0(N)\)-optimal |
| 377520.cn6 | 377520cn3 | \([0, -1, 0, -4878760, -313512122768]\) | \(-1769848555063681/5850659851882560\) | \(-42454224149958327812751360\) | \([2]\) | \(88473600\) | \(3.5965\) |
Rank
sage: E.rank()
The elliptic curves in class 377520.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.cn do not have complex multiplication.Modular form 377520.2.a.cn
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
