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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1300.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1300.a1 | 1300d1 | \([0, 1, 0, -7033, 224688]\) | \(153910165504/845\) | \(211250000\) | \([2]\) | \(1152\) | \(0.79071\) | \(\Gamma_0(N)\)-optimal |
1300.a2 | 1300d2 | \([0, 1, 0, -6908, 233188]\) | \(-9115564624/714025\) | \(-2856100000000\) | \([2]\) | \(2304\) | \(1.1373\) |
Rank
sage: E.rank()
The elliptic curves in class 1300.a have rank \(1\).
Complex multiplication
The elliptic curves in class 1300.a do not have complex multiplication.Modular form 1300.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.