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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 15210.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15210.v1 | 15210v3 | \([1, -1, 0, -315639, 65594205]\) | \(988345570681/44994560\) | \(158324327278940160\) | \([2]\) | \(290304\) | \(2.0622\) | |
15210.v2 | 15210v1 | \([1, -1, 0, -49464, -4196880]\) | \(3803721481/26000\) | \(91487337786000\) | \([2]\) | \(96768\) | \(1.5129\) | \(\Gamma_0(N)\)-optimal |
15210.v3 | 15210v2 | \([1, -1, 0, -19044, -9325692]\) | \(-217081801/10562500\) | \(-37166730975562500\) | \([2]\) | \(193536\) | \(1.8595\) | |
15210.v4 | 15210v4 | \([1, -1, 0, 171081, 249282333]\) | \(157376536199/7722894400\) | \(-27174886486861838400\) | \([2]\) | \(580608\) | \(2.4088\) |
Rank
sage: E.rank()
The elliptic curves in class 15210.v have rank \(1\).
Complex multiplication
The elliptic curves in class 15210.v do not have complex multiplication.Modular form 15210.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.