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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 308550.gr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308550.gr1 | 308550gr3 | \([1, 1, 1, -50198568263, 4328954400286781]\) | \(505384091400037554067434625/815656731648\) | \(22577900862110352000000\) | \([2]\) | \(597196800\) | \(4.4446\) | |
| 308550.gr2 | 308550gr4 | \([1, 1, 1, -50198084263, 4329042051718781]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-562006128682296485358484500000\) | \([2]\) | \(1194393600\) | \(4.7912\) | |
| 308550.gr3 | 308550gr1 | \([1, 1, 1, -621480263, 5902859038781]\) | \(959024269496848362625/11151660319506432\) | \(308685101676330221568000000\) | \([2]\) | \(199065600\) | \(3.8953\) | \(\Gamma_0(N)\)-optimal |
| 308550.gr4 | 308550gr2 | \([1, 1, 1, -125864263, 15058869022781]\) | \(-7966267523043306625/3534510366354604032\) | \(-97837511236398885523968000000\) | \([2]\) | \(398131200\) | \(4.2419\) |
Rank
sage: E.rank()
The elliptic curves in class 308550.gr have rank \(1\).
Complex multiplication
The elliptic curves in class 308550.gr do not have complex multiplication.Modular form 308550.2.a.gr
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
