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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4830t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4830.s4 | 4830t1 | \([1, 1, 1, 29, -127]\) | \(2691419471/9891840\) | \(-9891840\) | \([2]\) | \(1536\) | \(0.025141\) | \(\Gamma_0(N)\)-optimal |
| 4830.s3 | 4830t2 | \([1, 1, 1, -291, -1791]\) | \(2725812332209/373262400\) | \(373262400\) | \([2, 2]\) | \(3072\) | \(0.37171\) | |
| 4830.s1 | 4830t3 | \([1, 1, 1, -4491, -117711]\) | \(10017490085065009/235066440\) | \(235066440\) | \([2]\) | \(6144\) | \(0.71829\) | |
| 4830.s2 | 4830t4 | \([1, 1, 1, -1211, 14033]\) | \(196416765680689/22365315000\) | \(22365315000\) | \([2]\) | \(6144\) | \(0.71829\) |
Rank
sage: E.rank()
The elliptic curves in class 4830t have rank \(1\).
Complex multiplication
The elliptic curves in class 4830t do not have complex multiplication.Modular form 4830.2.a.t
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.
