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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 23400.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.v1 | 23400bf4 | \([0, 0, 0, -1731675, -874984250]\) | \(49235161015876/137109375\) | \(1599243750000000000\) | \([2]\) | \(294912\) | \(2.3655\) | |
| 23400.v2 | 23400bf3 | \([0, 0, 0, -1614675, 786766750]\) | \(39914580075556/172718325\) | \(2014586542800000000\) | \([2]\) | \(294912\) | \(2.3655\) | |
| 23400.v3 | 23400bf2 | \([0, 0, 0, -152175, -1520750]\) | \(133649126224/77000625\) | \(224533822500000000\) | \([2, 2]\) | \(147456\) | \(2.0190\) | |
| 23400.v4 | 23400bf1 | \([0, 0, 0, 37950, -189875]\) | \(33165879296/19278675\) | \(-3513538518750000\) | \([2]\) | \(73728\) | \(1.6724\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23400.v have rank \(1\).
Complex multiplication
The elliptic curves in class 23400.v do not have complex multiplication.Modular form 23400.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
