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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 10470.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10470.d1 | 10470d1 | \([1, 0, 0, -45435, 3726225]\) | \(-10372797669976737841/7632630000000\) | \(-7632630000000\) | \([7]\) | \(38808\) | \(1.4060\) | \(\Gamma_0(N)\)-optimal |
| 10470.d2 | 10470d2 | \([1, 0, 0, 182415, -207095505]\) | \(671282315177095816559/18919046447754148470\) | \(-18919046447754148470\) | \([]\) | \(271656\) | \(2.3790\) |
Rank
sage: E.rank()
The elliptic curves in class 10470.d have rank \(0\).
Complex multiplication
The elliptic curves in class 10470.d do not have complex multiplication.Modular form 10470.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
