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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 30446.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30446.a1 | 30446f3 | \([1, 0, 1, -3795071, -2955377838]\) | \(-6044818473864897584091625/274233188509844242432\) | \(-274233188509844242432\) | \([]\) | \(1003104\) | \(2.6858\) | |
| 30446.a2 | 30446f1 | \([1, 0, 1, -35601, 2916644]\) | \(-4989910628484015625/794743601010112\) | \(-794743601010112\) | \([3]\) | \(111456\) | \(1.5872\) | \(\Gamma_0(N)\)-optimal |
| 30446.a3 | 30446f2 | \([1, 0, 1, 239024, -10823394]\) | \(1510256987478812234375/924784759817371648\) | \(-924784759817371648\) | \([3]\) | \(334368\) | \(2.1365\) |
Rank
sage: E.rank()
The elliptic curves in class 30446.a have rank \(1\).
Complex multiplication
The elliptic curves in class 30446.a do not have complex multiplication.Modular form 30446.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
