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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 102960eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.co4 | 102960eh1 | \([0, 0, 0, 3093, -3768806]\) | \(1095912791/2055596400\) | \(-6137977960857600\) | \([2]\) | \(589824\) | \(1.7084\) | \(\Gamma_0(N)\)-optimal |
| 102960.co3 | 102960eh2 | \([0, 0, 0, -345387, -76461734]\) | \(1525998818291689/37268302500\) | \(111282554972160000\) | \([2, 2]\) | \(1179648\) | \(2.0550\) | |
| 102960.co2 | 102960eh3 | \([0, 0, 0, -773067, 150465274]\) | \(17111482619973769/6627044531250\) | \(19788248937600000000\) | \([4]\) | \(2359296\) | \(2.4016\) | |
| 102960.co1 | 102960eh4 | \([0, 0, 0, -5493387, -4955736134]\) | \(6139836723518159689/3799803150\) | \(11346151409049600\) | \([2]\) | \(2359296\) | \(2.4016\) |
Rank
sage: E.rank()
The elliptic curves in class 102960eh have rank \(1\).
Complex multiplication
The elliptic curves in class 102960eh do not have complex multiplication.Modular form 102960.2.a.eh
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
