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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 30420j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30420.c3 | 30420j1 | \([0, 0, 0, -2028, -24167]\) | \(16384/5\) | \(281499500880\) | \([2]\) | \(27648\) | \(0.90183\) | \(\Gamma_0(N)\)-optimal |
| 30420.c4 | 30420j2 | \([0, 0, 0, 5577, -162578]\) | \(21296/25\) | \(-22519960070400\) | \([2]\) | \(55296\) | \(1.2484\) | |
| 30420.c1 | 30420j3 | \([0, 0, 0, -62868, 6065917]\) | \(488095744/125\) | \(7037487522000\) | \([2]\) | \(82944\) | \(1.4511\) | |
| 30420.c2 | 30420j4 | \([0, 0, 0, -55263, 7588438]\) | \(-20720464/15625\) | \(-14074975044000000\) | \([2]\) | \(165888\) | \(1.7977\) |
Rank
sage: E.rank()
The elliptic curves in class 30420j have rank \(1\).
Complex multiplication
The elliptic curves in class 30420j do not have complex multiplication.Modular form 30420.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
