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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 302016.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.a1 | 302016a2 | \([0, -1, 0, -233508865, -1373272994399]\) | \(2278031600817539/131609088\) | \(81350451570728188772352\) | \([2]\) | \(102187008\) | \(3.4593\) | |
| 302016.a2 | 302016a1 | \([0, -1, 0, -15437825, -18833764959]\) | \(658275956099/132907008\) | \(82152724268664364204032\) | \([2]\) | \(51093504\) | \(3.1128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.a have rank \(1\).
Complex multiplication
The elliptic curves in class 302016.a do not have complex multiplication.Modular form 302016.2.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.
