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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 76313.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76313.b1 | 76313b4 | \([1, -1, 0, -407096, 100077275]\) | \(82483294977/17\) | \(1537792496873\) | \([2]\) | \(304128\) | \(1.7257\) | |
| 76313.b2 | 76313b2 | \([1, -1, 0, -25531, 1557192]\) | \(20346417/289\) | \(26142472446841\) | \([2, 2]\) | \(152064\) | \(1.3791\) | |
| 76313.b3 | 76313b1 | \([1, -1, 0, -3086, -27425]\) | \(35937/17\) | \(1537792496873\) | \([2]\) | \(76032\) | \(1.0326\) | \(\Gamma_0(N)\)-optimal |
| 76313.b4 | 76313b3 | \([1, -1, 0, -3086, 4183257]\) | \(-35937/83521\) | \(-7555174537137049\) | \([2]\) | \(304128\) | \(1.7257\) |
Rank
sage: E.rank()
The elliptic curves in class 76313.b have rank \(1\).
Complex multiplication
The elliptic curves in class 76313.b do not have complex multiplication.Modular form 76313.2.a.b
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.
