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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 70560dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.cb3 | 70560dh1 | \([0, 0, 0, -8752233, 9963867368]\) | \(13507798771700416/3544416225\) | \(19455413172973646400\) | \([2, 2]\) | \(2949120\) | \(2.6859\) | \(\Gamma_0(N)\)-optimal |
| 70560.cb4 | 70560dh2 | \([0, 0, 0, -7680603, 12494843102]\) | \(-1141100604753992/875529151875\) | \(-38446458459514176960000\) | \([2]\) | \(5898240\) | \(3.0325\) | |
| 70560.cb2 | 70560dh3 | \([0, 0, 0, -9832683, 7348530098]\) | \(2394165105226952/854262178245\) | \(37512577712683129674240\) | \([2]\) | \(5898240\) | \(3.0325\) | |
| 70560.cb1 | 70560dh4 | \([0, 0, 0, -140026908, 637771873088]\) | \(864335783029582144/59535\) | \(20914528312258560\) | \([2]\) | \(5898240\) | \(3.0325\) |
Rank
sage: E.rank()
The elliptic curves in class 70560dh have rank \(0\).
Complex multiplication
The elliptic curves in class 70560dh do not have complex multiplication.Modular form 70560.2.a.dh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
